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Question

Let A = $open parentheses table row 1 cell negative 1 end cell 1 row 2 1 cell negative 3 end cell row 1 1 1 end table close parentheses$ and (10) B = $open parentheses table row 4 2 2 row cell negative 5 end cell 0 alpha row 1 cell negative 2 end cell 3 end table close parentheses$ . If B is the inverse of matrix A, then $alpha$ is

– 2
– 1
2
5

hint Hint:

$begin mathsize 14px style We space have comma straight A space equals space open square brackets table row 1 cell negative space 1 end cell 1 row 2 1 cell negative space 3 end cell row 1 1 1 end table close square brackets space and space 10 space straight B space equals space open square brackets table row 4 2 2 row cell negative space 5 end cell 0 straight alpha row 1 cell negative space 2 end cell 3 end table close square brackets Given space that space straight B space is space inverse space of space straight A. therefore space AB space equals space straight I rightwards double arrow space straight A open parentheses 10 straight B close parentheses space equals space 10 straight I space space space space space space space space space space space space space open square brackets multiplying space by space 10 space on space both space sides close square brackets rightwards double arrow space open square brackets table row 1 cell negative space 1 end cell 1 row 2 1 cell negative space 3 end cell row 1 1 1 end table close square brackets open square brackets table row 4 2 2 row cell negative space 5 end cell 0 straight alpha row 1 cell negative space 2 end cell 3 end table close square brackets space equals space open square brackets table row 10 0 0 row 0 1 0 row 0 0 1 end table close square brackets rightwards double arrow space space space space space space space space space space space space space space space space space space space open square brackets table row 10 0 cell 5 space minus space straight alpha end cell row 0 10 cell straight alpha space minus space 5 end cell row 0 0 cell straight alpha space plus space 5 end cell end table close square brackets space equals space open square brackets table row 10 0 0 row 0 1 0 row 0 0 1 end table close square brackets rightwards double arrow 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 straight alpha space equals space 5 end style$

The correct answer is: 5

Given matrix A = $open parentheses table row 1 cell negative 1 end cell 1 row 2 1 cell negative 3 end cell row 1 1 1 end table close parentheses$ and (10) B = $open parentheses table row 4 2 2 row cell negative 5 end cell 0 alpha row 1 cell negative 2 end cell 3 end table close parentheses$ and B is the inverse of matrix A, then we need to find $alpha$ is.

Therefore, $alpha equals 5.$

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