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Midterm 1

# Midterm 1 - Math 211 Linear Algebra Midterm 1 Spring 2011...

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Math 211: Linear Algebra Midterm 1 Spring 2011 Time: 90 min. Last Name First Name Special Notes: a) Textbooks, notes, notecards, calculators, cell phones, electronic devices, etc. are NOT allowed. b) To obtain credit you need to show all your work. Justify all of your claims and arguments fully, and write clearly and legibly. c) Use the backs of the pages if you need extra space. Problem 1 20 Problem 2 20 Problem 3 25 Problem 4 25 Problem 5 25 Total 115 Honor Code Statement: Sign after completing your exam. I have neither given nor received aid on this examination. Signature 1

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(1) Suppose that A = 1 - 2 - 2 5 and AB = - 1 2 c 6 - 9 d , and let B = h ~ b 1 ~ b 2 ~ b 3 i . (a) Explicitly find ~ b 1 and ~ b 2 . (b) Suppose that ~ b 3 = ~ b 1 + ~ b 2 . (i) Is the matrix equation h ~ b 1 ~ b 2 i x = ~ b 3 consistent? (ii) Explicitly find c and d . 2
(2) (a) Suppose A is a 3 × 3 matrix and that ~ b is a fixed vector in R 3 . If the matrix equation A x = ~ b has a unique solution, explain why the columns of A must span R 3 .

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