First, let's calculate A^2, 4A, and 5I2.

Given matrix A is:
A = [3 -1]
[2 1]

To find A^2, we multiply matrix A 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]

4A is simply 4 times matrix A:

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

5I2 is 5 times the 2x2 identity matrix:

5I2 = 5 * [1 0]
[0 1]
= [5 0]
[0 5]

Now, let's calculate A^2 - 4A + 5I2:

A^2 - 4A + 5I2 = [7 -4] - [12 -4] + [5 0]
[8 0] [8 4] [0 5]
= [-5 0]
[0 5]

So, A^2 - 4A + 5I2 = 0.

Now, let's find A^4. We already have A^2, so we just need to multiply A^2 by itself:

A^4 = A^2 * A^2

Question

First, let's calculate A^2, 4A, and 5I2.

Given matrix A is:
A = [3 -1]
    [2  1]

To find A^2, we multiply matrix A 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]

4A is simply 4 times matrix A:

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

5I2 is 5 times the 2x2 identity matrix:

5I2 = 5 * [1 0]
          [0 1]
     = [5 0]
       [0 5]

Now, let's calculate A^2 - 4A + 5I2:

A^2 - 4A + 5I2 = [7 -4] - [12 -4] + [5 0]
                 [8  0]   [8   4]   [0 5]
               = [-5 0]
                 [0  5]

So, A^2 - 4A + 5I2 = 0.

Now, let's find A^4. We already have A^2, so we just need to multiply A^2 by itself:

A^4 = A^2 * A^2

Knowee AI · Accepted Answer