Math 54 quiz 2 compute the product ab suppose that a is an

Question

MATH 54 QUIZ 2-

1. Compute the product AB where

2. Are the following collections of vectors linearly independent? Justify your answer.

3. Is the following matrix invertible? If so, find its inverse.

4. State 6 conditions of the invertible matrix theorem.

5. True or false? Justify your answer.

(i) If the columns of an n × n matrix A are linearly independent, then they span Rⁿ.

(ii) Let A be a 2 × 3 matrix. There exists a 3 × 2 matrix C such that CA = I₃.

6. Suppose that A is an n × n matrix such that A⁴ = A · A · A · A is invertible. Prove that A invertible.

7. Write anything you like here (comments, questions, suggestions, etc).