ข้อสอบ PAT 1 - กุมภาพันธ์ 2562

ข้อ 45

กำหนดให้ straight B equals open square brackets table row straight a 2 cell negative 1 end cell row 3 straight b 2 row cell negative 1 end cell 3 straight c end table close square brackets เมื่อ straight a comma straight b และ straight c เป็นจำนวนจริง และ straight C equals open square brackets table row cell 1 third end cell 0 0 row 0 cell negative 1 half end cell 0 row 0 0 1 end table close square brackets

ถ้า straight A เป็นเมทริกซ์ที่มีมิติ 3 cross times 3 โดยที่ AB equals straight C และ straight A open square brackets table row cell 4 straight a plus 1 end cell row cell 5 straight b plus 2 end cell row cell 4 straight c plus 3 end cell end table close square brackets equals open square brackets table row 1 row cell negative 2 end cell row 3 end table close square brackets

แล้วค่าของ straight a plus straight b plus straight c เท่ากับเท่าใด

รีวิว - เสียงตอบรับจากผู้เรียน
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด

เฉลยข้อสอบ

begin mathsize 12px style space จากโจทย ์ space space space space space A B space equals space C space จะได ้ space space space space space space space space A to the power of negative 1 end exponent times open parentheses A B close parentheses space equals space A to the power of negative 1 end exponent times C space space space space space space space space space space space space space space space space space space space space space space space space space space space space space I B space equals space A to the power of negative 1 end exponent times C space space space space space space space space space space space space space space space space space open parentheses I B close parentheses times C to the power of negative 1 end exponent space equals space open parentheses A to the power of negative 1 end exponent C close parentheses times C to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space up diagonal strike I B C to the power of negative 1 end exponent space equals space A to the power of negative 1 end exponent up diagonal strike I space space space space space space space space space space space space space space space space space space space space space space space space space A to the power of negative 1 end exponent space equals space B C to the power of negative 1 end exponent space rightwards arrow space box enclose 1 end style

begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style

begin mathsize 12px style space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator begin display style 1 third open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses open parentheses 1 close parentheses end style end fraction open square brackets table row cell fraction numerator negative 1 over denominator 2 end fraction end cell 0 0 row 0 cell 1 third end cell 0 row 0 0 cell fraction numerator negative 1 over denominator 6 end fraction end cell end table close square brackets to the power of t space end style

begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style

begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style

begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style

begin mathsize 12px style space space space space space space space space space space space space space space space space space space space space space space space space space space I space open square brackets table row cell 4 a plus 1 end cell row cell 5 b plus 2 end cell row cell 4 c plus 3 end cell end table close square brackets equals space A to the power of negative 1 end exponent space open square brackets table row 1 row cell negative 2 end cell row 3 end table close square brackets end style

begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style

begin mathsize 12px style จะได ้ 4 a plus 1 space equals space 3 a plus 5 space space space space space space space space space 5 b plus 2 space equals space 4 b plus 15 space space space space space space space space space space 4 c plus 3 space equals space 3 c plus 9 space space space space space space space a space equals space 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space b space equals space 13 space space space space space space space space space space space space space space space space space space space space space space space space space space space space c space equals space 6 ด ั งน ั้ น space space space space space space space space space space a plus b plus c space equals space 4 plus 13 plus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 23 end style

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