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Assignment 4 - MATH 223 Linear Algebra Winter 2010...

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MATH 223, Linear Algebra Winter, 2010 Assignment 4, due in class Monday, February 8, 2010 1. Find a basis for each of the row space, column space and null space of the following matrix A over the complex numbers. What is its rank? Express each row of A as a linear combination of the rows in your basis for the row space; express each of the columns of A as a linear combination of the vectors in your basis for the column space. A = 1 2 i 2 + 4 i 1 + 8 i 4 + 14 i 1 - i 3 + 2 i 7 + i 12 + 7 i 23 + 9 i i 0 - 2 - 2 + i - 3 + 2 i 4 - 1 + i 10 i 1 + 11 i 4 + 22 i . 2. Let V = Z 4 2 and W 1 = Span 1 0 1 0 , 0 1 0 1 and W 2 = Span 0 1 1 0 , 1 0 0 1 and be subspaces of V . Find a basis for W 1 + W 2 and one for W 1 W 2 . 3. Let V = C 5 and W 1 = Span 1 i 1 i
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