Find the matrix A such that `[{:(2,-1),(1,0),(-3,4):}].A=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}].`

Explanation

Clearly, the product is a `3xx2` matrix and the prefactor is a `3xx2` matrix. So, A must be a `2xx3` matrix.
Let `A=[{:(x,y,z),(u,v,w):}].`
Then the given equation becomes
`[{:(2,-1),(1," "0),(-3," "4):}][{:(x,y,z),(u,v,w):}]=[{:(-1,-8,-10),(1,-2,-5),(9,22," "15):}]`
or `[{:(2x-u,2y-v,2z-w),(x,y,z),(-3x+4u,-3y+4v,-3z+4w):}]=[{:(-1,-8,-10),(" "1,-2,-5),(" "9," "22," "15):}].`
So, by the definition of equal matrices, we have
`2x-u=-1,2y-v=-8,2z-w=-10,x=-2,z=-5.`
`:." "x=1,y=-2,z=-5,u=3,v=4" and "w=0.`