2011WT2midterm1.solutions - 1 University of British...

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1 University of British Columbia Math 307, Section 201 Midterm 1 Date:February 13, 2012 Time:12:00 - 12:50pm Name (print): Student ID Number: Signature: Instructor:Richard Froese Instructions: 1. No notes, books or calculators are allowed. 2. Read the questions carefully and make sure you provide all the information that is asked for in the question. 3. Show all your work. Answers without any explanation or without the correct accompanying work could receive no credit, even if they are correct. 4. Answer the questions in the space provided. Continue on the back of the page if necessary. QuestionMarkMaximum 112 26 312 412 Total40
2 1. Suppose thatAis a matrix with R(A) = span1210,1021R(AT ) = span1111, 1 1 -1 -1 [2] (a) How many rows and how many columns doesAhave?
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[2] (b) What are rank(A), dim(N(A)) and dim(N(AT))?
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[2] (c) For what numbersaandbare the vectors [2, a,-1,0]Tand [1,0,-1, b]T contained in N(AT )?
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[3]

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