Question

Given the matrices `A=[(5,7),(-1,6), (3,-9)], B=[(8,3), (5,1), (4,4)], C=[(0,4),(-2,5), (7,-1)], D[(6,2), (9,0), (-3,0)]`, how do you find `3C-4A+B`?

Answer 1

`[(-12 ,-13), (3,-8), (13,37)]`

Explanation:

These are all `3xx2` matrices and are therefore compatible for the multiplication and addition that is asked.
`A=[(5,7),(-1,6), (3,-9)], B=[(8,3), (5,1), (4,4)], C=[(0,4),(-2,5), (7,-1)], D[(6,2), (9,0), (-3,0)]`,

`3C=3[(0,4),(-2,5), (7,-1)] = [(0,12),(-6,15), (21,-3)]`

`-4A = -4[(5,7),(-1,6), (3,-9)] = [(-20,-28),(4,-24), (-12,36)]`

`3C -4A +B = [(0,12),(-6,15), (21,-3)] + [(-20,-28),(4,-24), (-12,36)]+[(8,3), (5,1), (4,4)]`

`=[(-12 ,-13), (3,-8), (13,37)]`

Answer 2

`3C - 4A + B`

`=color(blue)3[(0,4), (-2,5), (7,-1)] - color(red)4 [(5,7), (-1,6), (3,-9)] + [(8,3),(5,1),(4,4)]`

`= [(color(blue)3*0,color(blue)3*4), (color(blue)3*-2,color(blue)3*5), (color(blue)3*7,color(blue)3*-1)] - [(color(red)4*5,color(red)4*7), (color(red)4*-1,color(red)4*6), (color(red)4*3,color(red)4*-9)] + [(8,3),(5,1),(4,4)]`

`=[(0,12), (-6,15), (21,-3)] - [(20,28), (-4,24), (12,-36)] + [(8,3),(5,1),(4,4)]`

`=[(-20,-16), (-2,-9), (9,33)] + [(8,3),(5,1),(4,4)]`

`=[(-12,-13), (3,-8), (13,37)]`