Assignment3

# Assignment3 - MATH 223 Linear Algebra Fall 2010 Assignment...

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Unformatted text preview: MATH 223, Linear Algebra Fall, 2010 Assignment 3, due in class Friday, September 24, 2010 1. Let V = M 2 ( R ) be the real vector space of 2 × 2 matrices with real entries. For each of the following subsets of V , decide if it is independent, if it is a spanning set for V , and/or if it is a basis for V . Justify your answers. (a) { 1 3 2- 1 ¶ , 2 0 5 0 ¶ , 4 1- 1 ¶ } . (b) { 1 1 1 1 ¶ , 1 1- 1- 1 ¶ , 1- 1 1- 1 ¶ , 1 2 3 5 ¶ } . (c) { 1 0 0 0 ¶ , 1 1 0 0 ¶ , 1 1 1 0 ¶ , 1 1 1 1 ¶ , 0 1 1 1 ¶ } . 2. Find a basis for each of the null space, row space and column space of the following matrix over C . A = 1 2- i- 3 + 2 i 3 i- 1 + i 2- 2 i- 2- 3 + i 1 + i 2- 3 + i- 3 + i- 1- 3 i 2 i 3 + 6 i- 6- 10 i- 7 + 3 i 6 + 5 i . Express each row of A as a linear combination of the vectors in your basis for the row space, and express each column of A as a linear combination of the vectors in your basis for the column space....
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