Question

Give a 3 × 3 elementary matrix E which will carry out the row operation (-7) → Test that E actually works for carrying out this row operation by computing the product EA for the matrix

Answer 1

To carry out the row operation (-7), create a 3x3 elementary matrix E and compute the product EA to test if it works.

Step-by-step explanation:

To carry out the row operation (-7), we need to create a 3x3 elementary matrix E.

An elementary matrix is obtained from the identity matrix by performing a single elementary row operation.

In this case, to multiply the third row by -7, we can create the following elementary matrix:

E = [[1, 0, 0], [0, 1, 0], [0, 0, -7]]

To test if E works, we can compute the product EA, where A is the given matrix:

EA = [[1, 0, 0], [0, 1, 0], [0, 0, -7]] * [[5, 10, 15, 20], [-1, -8, 0, 0], [-7, -2, -9, -15]] = [[5, 10, 15, 20], [-1, -8, 0, 0], [49, 14, 63, 105]]

As we can see, the third row of the product has been multiplied by -7, confirming that the matrix E successfully carries out the row operation (-7).