How do you find missing values in a matrix?

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.

1 Answer
Apr 5, 2018

color(blue)(a=-1)

color(blue)(b=10)

Explanation:

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)