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