Question

Hi there! Can you solve this matrix equation? (See picture). Thanks!

Answer 1

Given `4X+5A= B`, `A = [(0,-3),(-6,-8),(5,-9)]` and `B = [(4,-8),(2,-1),(9,1)]`

Solve the first equation for X:

`X = 1/4B+ -5/4A`

Compute `1/4B`:

`1/4B = [(1,-2),(1/2,-1/4),(9/4,1/4)]`

Compute `-5/4A`:

`-5/4A = [(0,15/4),(15/2,10),(-25/4,45/4)]`

`X_(1,1) = 1+0 = 1`

`[(1, )]`

`X_(1,2) = -2+15/4 = 7/4`

`[(1,7/4)]`

`X_(2,1) = 1/2+15/2 = 8`

`[(1,7/4),(8, )]`

`X_(2,2) = -1/4+10 = 39/4`

`[(1,7/4),(8, 39/4)]`

`X_(3,1) = 9/4-25/4 = -4`

`[(1,7/4),(8, 39/4),(-4, )]`

`X_(3,2) = 1/4+45/4 = 46/4`

`X = [(1,7/4),(8, 39/4),(-4, 46/4)]`

Answer 2

The answer is `((1,7/4),(8,39/4),(-4,23/2))`

Explanation:

The matrix equation is

`4X+5A=B`

`X=1/4(B-5A)`

`A=((0, -3),(-6,-8),(5,-9))`

`B=((4, -8),(2,-1),(9,1))`

`B-5A=((4, -8),(2,-1),(9,1))-5((0, -3),(-6,-8),(5,-9))`

`=((4,7),(32,39),(-16,46))`

Therefore,

`X=1/4(B-A)=1/4((4,7),(32,39),(-16,46))`

`=((1,7/4),(8,39/4),(-4,23/2))`