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341hw9 - 1 1 1 1 2 2 2 3 4 4 Let A be the matrix 1 3-2 1 2...

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Homework 9, due Friday November 4th , in class 1. Suppose x 1 , x 2 , and x 3 are linearly independent vectors in R n . Define y 1 = x 1 + x 2 , y 2 = x 2 + x 3 , y 3 = x 3 + x 1 . Are y 1 , y 2 , and y 3 linearly independent? Prove your answer. 2a. Are the vectors v 1 = 2 1 , v 2 = 5 3 , v 3 = 7 - 3 linearly independent? 2b. Write v 3 as a linear combination of v 1 and v 2 . 3. Find the coordinates of the vector 3 2 5 with respect to the ordered basis
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Unformatted text preview: 1 1 1 , 1 2 2 , 2 3 4 . 4. Let A be the matrix 1 3-2 1 2 1 6 2 3 4 8 11 . 4a. Find a basis for the null space of A . 4b. Find a basis for the row space of A . 4c. Find a basis for the column space of A . 1...
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