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2008_Spring_midterm_2_solutions

# 2008_Spring_midterm_2_solutions - Name TA Math 20F Midterm...

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Name: PID: TA: Sec. No: Sec. Time: Math 20F Midterm Exam 2 Solutions May 21, 2008 Turn off and put away your cell phone. You may use one page of notes, but no calculators, books or other assistance. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # Points Score 1 10 2 8 3 10 4 12 Σ 40

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1. Consider the following elementary row operations on the set of 3 × 3 matrices: (1) Add 3 times the first row to the third row (2) Interchange the second and third rows (3) Multiply the first row by 7. Let E 1 , E 2 , and E 3 be the corresponding elementary matrices. a. Write down all the matrices E 1 , E 2 , E 3 , E 1 1 , E 1 2 , and E 1 3 . Solution: E 1 = 1 0 0 0 1 0 3 0 1 , E 2 = 1 0 0 0 0 1 0 1 0 , E 3 = 7 0 0 0 1 0 0 0 1 , E 1 1 = 1 0 0 0 1 0 - 3 0 1 , E 1 2 = 1 0 0 0 0 1 0 1 0 , E 1 3 = 1 /
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