341hw8 - 4a 1 1 1 1 1 0 2 5-11 42 0 0-1 8 37 0 0 3 99 7 7 7...

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Homework 8, due Friday October 28th , in class 1. Find the inverse of the matrix 1 2 3 2 5 10 1 4 12 . 2a. Find the inverse of - x 1 0 0 1 - x 0 0 0 0 - x 1 0 0 1 - x (the algebra will be a little messy, but it won’t take very many steps). Your answer will of course involve x . 2b. For what values of x is your answer in 2a undefined? 3. Define A = 1 - 1 1 - 1 1 - 1 4 2 0 0 2 5 . 3a. Determine the null space of the matrix A . 3b. Are the columns of A linearly independent? 4. Using appropriate shortcuts, find the determinant of each of the following matrices using as little computation as possible.
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Unformatted text preview: 4a. 1 1 1 1 1 0 2 5-11 42 0 0-1 8 37 0 0 3 99 7 7 7 7 9 . 1 4b. 3-8 12 7-9 2 1-5 17 40 8 6-1 9 112 3-8 12 7-9 11 13 71-4 12 5. Given the vectors v 1 = 1 1 2 and v 2 = 1-1 in R 3 , find a vector v 3 such that { v 1 , v 2 , v 3 } is a basis for R 3 . (There may be many possible correct answers. Make sure you justify your answer appropriately.) 2...
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This note was uploaded on 12/07/2011 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

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341hw8 - 4a 1 1 1 1 1 0 2 5-11 42 0 0-1 8 37 0 0 3 99 7 7 7...

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