If A= [2−185−32]%0D%0A[%0D%0A2%0D%0A8%0D%0A−%0D%0A3%0D%0A−%0D%0A1%0D%0A5%0D%0A2%0D%0A]%0D%0A and B= [−10035−2]%0D%0A[%0D%0A−%0D%0A1%0D%0A0%0D%0A5%0D%0A0%0D%0A3%0D%0A−%0D%0A2%0D%0A]%0D%0A , what is 4A+3B? Solve algebraically, showing all steps.

Answer 1

To find the expression 4A + 3B, we need to multiply each element in matrix A by 4 and each element in matrix B by 3, and then add the corresponding elements together.

First, let's find 4A:
4A = 4 * [2 -1 8 -3 -1] = [8 -4 32 -12 -4]
[5 2 10 -6 2]

Next, let's find 3B:
3B = 3 * [-10 3 -2] = [-30 9 -6]
[0 15 9]
[-2 -6 -3]

Now, let's add the corresponding elements together:
4A + 3B = [8 -4 32 -12 -4] + [-30 9 -6] = [-22 5 26 -12 -4]
[5 2 10 -6 2] [0 15 9] [5 17 9]
[-2 -6 -3]

Therefore, 4A + 3B is equal to:
[-22 5 26 -12 -4]
[5 17 9]
[-2 -6 -3]