Question

Find matrix A such that `((2,-1),(1,0),(-3,4))A = ((-1, -8),(1, -2),(9,22))`

Answer 1

Given

`[(2,-1),(1,0),(-3,4)]A = [(-1, -8),(1, -2),(9,22)]`

A should be 2 x 2 order

Let A = `[(a,b),(c ,d)]`

Now

`[(2,-1),(1,0),(-3,4)][(a,b),(c,d)] = [(-1,-8),(1,-2),(9,22)]`

By solving and comparing, we get

2a - c  = 1....(i)

2b - d = -8....(ii)

a = 1....(iii)

b = -2...(iv)

sub a= 1 in (i)

c = 3 

and sub b =  -2 in (iii)

d = 4

so A matrix

A = `[(1,-2),(3,4)]`