Sure, let's solve this step by step.

First, let's define the matrix A and the identity matrix I:

A = [3 -1]
[2 1]

I = [1 0]
[0 1]

Next, we calculate A^2, which is the matrix A multiplied by itself:

A^2 = A * A
= [3 -1] * [3 -1]
[2 1] [2 1]
= [(3*3 + -1*2) (3*-1 + -1*1)]
[(2*3 + 1*2) (2*-1 + 1*1)]
= [7 -4]
[8 0]

Then, we calculate 4A:

4A = 4 * A
= 4 * [3 -1]
[2 1]
= [12 -4]
[8 4]

Next, we calculate 5I:

5I = 5 * I
= 5 * [1 0]
[0 1]
= [5 0]
[0 5]

Finally, we calculate A^2 - 4A + 5I:

A^2 - 4A + 5I = [7 -4] - [12 -4] + [5 0]
[8 0] [8 4] [0 5]
= [-5 0]
[0 5]

So, A^2 - 4A + 5I = 0, as required.

Question

Sure, let's solve this step by step.

First, let's define the matrix A and the identity matrix I:

A = [3 -1]
    [2  1]

I = [1 0]
    [0 1]

Next, we calculate A^2, which is the matrix A multiplied by itself:

A^2 = A * A
    = [3 -1] * [3 -1]
      [2  1]   [2  1]
    = [(3*3 + -1*2)  (3*-1 + -1*1)]
      [(2*3 + 1*2)   (2*-1 + 1*1)]
    = [7 -4]
      [8  0]

Then, we calculate 4A:

4A = 4 * A
   = 4 * [3 -1]
         [2  1]
   = [12 -4]
      [8   4]

Next, we calculate 5I:

5I = 5 * I
   = 5 * [1 0]
         [0 1]
   = [5 0]
     [0 5]

Finally, we calculate A^2 - 4A + 5I:

A^2 - 4A + 5I = [7 -4] - [12 -4] + [5 0]
                [8  0]   [8   4]   [0 5]
              = [-5 0]
                [0  5]

So, A^2 - 4A + 5I = 0, as required.

Knowee AI · Accepted Answer