Rules/Suggestions: Write with a dark pencil, so that your work is visible. You are graded on your work, not just answers. Even if you do calculations in your head or on scratch paper, show work if space is provided. Write the final answer in the box. 1. Given 3 1 5 7 4 0 -5 , -4 21, 0o -21, 1 3 -8 6 -3 1 -1 answer the following questions. If the operation is impossible, state that and the reason why. (1.1) (3 points) 34 BT (1.3) (3 points) ABT Answer: Answer: (1.2) (3 points) A+ 5C (1.4) (3 points) AB Answer: Answer: 2. The following question makes you think about matrix products. When you perform the multiplication of a 2 X 2 matrix by a 2 x 2 matrix, you do multiplication 8 times and addition 4 times: e How many times do you perform multiplication and addition if you multiply the following: ae+bg af+bh ce+dg cf+dh (2.1) (3 points) a 2 x 3 matrix by a 3 X 1 matrix (2.2) (3 points) a 2 x 3 matrix by a 3 X 2 matrix (2.3) (3 points) a 2 x 3 matrix by a 3 x 3 matrix (2.4) (3 points) a 2 x 3 matrix by a 3 x 20 matrix (2.5) (3 points) a 3 x 3 matrix by a 3 x 20 matrix 3. Consider the matrices A= 1 3 1 0 4 and B= |4 5 3 5 2 2 1 (3.1) (3 points) Perform the computation C' = AB. Answer: (3.2) (3 points) Suppose the first matrix the represents the number of tablespoons (tbs.) of caramel and chocolate in different deserts. The second matrix is how many of each desert were sold at Cafe A and Cafe B. Explain what the lower right entry, cas, of the answer to given in the previous part would mean in this context. Discuss both the calculations involved and the result.