Question

Let a = 1 1 1 1 2 3 1 4 5 and d = 2 0 0 0 2 0 0 0 5. Compute ad and da. Find a 3x3 matrix b that is not the identity matrix.

Answer 1

To compute the product of matrices ad and da, multiply the rows of one matrix by the columns of the other matrix. To find a non-identity 3x3 matrix b, choose a matrix with at least one element different from 1 in each row and column.

Step-by-step explanation:

To compute the product of matrices ad and da, we need to multiply the elements of the matrices following the rules of matrix multiplication.

For ad:

a = 1 1 1 1 2 3 1 4 5

d = 2 0 0 0 2 0 0 0 5

To compute ad, we multiply the rows of a by the columns of d:

ad = (1x2 + 1x0 + 1x0) (1x0 + 1x2 + 1x0) (1x0 + 1x0 + 1x5) = 2 2 5

For da:

d = 2 0 0 0 2 0 0 0 5

a = 1 1 1 1 2 3 1 4 5

To compute da, we multiply the rows of d by the columns of a:

da = (2x1 + 0x1 + 0x2) (2x1 + 0x1 + 0x2) (2x1 + 0x3 + 0x4) = 2 2 2

To find a 3x3 matrix b that is not the identity matrix, we can choose any matrix that has at least one element different from 1 in each row and column. For example:

b = 1 0 0

0 2 0

0 0 1