hw9(1) - A ) T x 1 x 2 x 3 x 4 x 5 = A · x 1 x 2 x 3 x 4 x...

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MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011, HW#9 Due date: Teusday, June 28th Note : All the problems below are related to Theorem 3.16 on Page 191. So please read the understand Theorem 3.16 before doing the following home- work. 1. Problem 5 Page 196. 2. Problem 7 on Page 197. 3. Problem 9 on Page 197. 4. Problem 12 on Page 197. 5. Problem 13 on Page 197. 6. Let A = 1 - 2 0 1 0 1 - 2 - 1 0 - 1 - 2 4 1 - 1 1 3 - 6 3 6 0 . (a) Find a basis for the row space of A (i.e.the space generated by the row vectors of A ). (b) Find a basis for the column space of A (i.e.the space generated by the column vectors of A ). . (c) Consider the linear defined by T : R 5 R 4 defined by (i.e. T is the left multiplication transformation associated to
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Unformatted text preview: A ) T x 1 x 2 x 3 x 4 x 5 = A · x 1 x 2 x 3 x 4 x 5 , where A is given above. Find a basis for N ( T ) (the nullspace of T ) and a basis for R ( T ) (the range of T ). 1 7. Suppose A has row reduced form R , A = 1 2 1 b 2 a 1 8 ? ? ? ? , R = 1 2 0 3 0 0 1 2 0 0 0 0 . (a) What are the numbers a and b ? (b) What can you say about the third row of A ? (c) Describe the solution space of AX = 0. 2...
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This note was uploaded on 02/21/2012 for the course MATH 4377 taught by Professor Staff during the Summer '08 term at University of Houston.

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hw9(1) - A ) T x 1 x 2 x 3 x 4 x 5 = A · x 1 x 2 x 3 x 4 x...

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