(a) Consider the following matrix equation: X + 6. 8. Use your calculator to find the matrix X. Then, find X by hand and check that your calculator didn't make a mistake. (b) Compute the matrix product by hand and then with a calculator: C9679 -2 4 1

-6 -5 4 Compute 2(2A – 3B) if matrix A = 1 and matrix B = 3 - 5 2 - 5 2(2A – 3B) = (Simplify your answers.)

2x + y =2, 4x+3y=7. Find the solution(x=?,y=?) by using the Matrix calculation method including the inverse matrix.

What is the inverse of the matrix: -1 3 2 -1 2 0 -1 1 ?

d) Consider the following matrices: 1 -3 A = 2 -4 and B- Find: i) A- ii) (2AB) - 2.

Consider the three equations: - 2y = -1,3x4z = -1 and 2x + 2y + z = 2. Write these in the form of Ax = b. Which of the following are true of the matrices A and b? A22 = 0 A31 = -2 b₂ = -1 b3 = 2 A13 = 0

On the augmented matrix A below , perform all three row operations in the order given, ((a) followed by (b) followed by (c)) and then write the resulting augmented matrix.

Write equations 3x – 4y = 7 and 2x + y = 1 as the matrix equation a () - () and then: Calculate the inverse matrix A-1.

Let A be a 2 x 3 matrix and B be a 3 x 2. Which of the following gives a 3 x 3 matrix as a result? Select one alternative: BA A+BT AT +B AB

The figure to the right shows the letter L in a rectangular coordinate system. The figure can be represented by the matrix B, shown to the right. Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0,9), to the starting point, (0,0). Use these ideas to complete parts (a) and (b) below. a. If A = AB - 1 0 [!!] 0 1 find AB. (Simplify your answer.) b. Graph the object represented by matrix AB. What effect does the matrix multiplication have on the letter L represented by matrix B? Choose the correct graph below. A. O B. Rotates the letter L about the origin. Reflects the letter L across the x-axis. O C. Q 077 11 0 B-[07718] 001 199 B= Reflects the letter L across the y-axis.