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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 Spring '07
 Loveys
 Linear Algebra, Algebra, Matrices, Vector Space, Sets, −, real vector space, .

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