Test review please help

Question

Answer 1

(20)

The matrix operation is

The scalar product of a real number, r, and a matrix A is the matrix rA.

Each element of matrix rA is r times its corresponding element in A.

Therefore .

Answer 2

(21)

The Matrix A is .

A² = A*A

Therefore .

Answer 3

(22)

Now consider the augmented form of matrix

Now Perform .

We have brought the matrix to row-echelon form.

The corresponding system is

z = 9

y = 5 and

-2x + 8y + z = 1

-2x + 8*5 + 9 = 1

-2x + 40 + 9 = 1

-2x = 1 - 49

-2x = -48

x = 24

Therefore the solution of (x y z) is (24 5 9).