Question

Find matrix X so that `x ((1,2,3),(4,5,6)) = ((-7,-8,-9),(2,4,6))`.

Answer 1

Given : `x [[1,2,3],[4,5,6]]= [[-7,-8,-9],[2,4,6]]` 

Since `[[1,2,3],[4,5,6]]` is a 2 × 3 matrix and the product is also a 2 × 3 matrix so, X will be a 2 × 2 matrix.

Let 

x= `[[x,y],[a,b]]`.Then the given equation becomes,

`[[x,y],[a,b]] [[1,2,3],[4,5,6]]= [[-7,-8,-9],[2,4,6]]` 

`⇒ [[x+4x,2x+5y, 3x+6y],[a+4b,2a+5b,3a+6b]] =[[-7,-8,-9],[2,4,6]]`

⇒ ` x+4y =-7,2x +5y = -8,3x +6y = -9`

     `a+4b = 2, 2a +5b = 4, 3a +6b = 6`

⇒ `x = 1, y =-2, a= 2, b=0`

Thus, X will be 

`x=[[1,-2],[2,0]]`.