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)#