How do you find missing values in a matrix?

Question

The matrix I have is given by $M=((1,a),(0,2))$ , and the image of the point $(b,5)$ under $M$ is $(5,b)$ . I need to find the values of $a$ and $b$ .

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Answer 1 · 2018-04-05T09:41:15

$color(blue)(a=-1)$

$color(blue)(b=10)$

We have:

$bbM=[(1,a),(0,2)]$

$bbA=[(b),(5)]$

$bbB=[(5),(b)]$

We are told:

$bb(MA)=bbB$

$bb(MA)=[(1,a),(0,2)][(b),(5)]=[(b+5a),(10)]$

$:.$

$[(b+5a),(10)]=bbB=[(5),(b)]$

$[(b+5a),(10)]=[(5),(b)]$

$:.$

$b+5a=5color(white)(88)[1]$

$10=bcolor(white)(88)[2]$

So $b=10$

Substituting $b=10$ in $[1]$

$10+5a=5=>a=-1$

$color(blue)(a=-1)$

$color(blue)(b=10)$