Homework 6 - º ²³ ´ µ µ µ » ¸ are linearly...

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Homework 6 (Due Monday, December 6, 2010) 1. Each of the following gives you a set of points (vectors in x-y plane) which satisfy the given equation. In each case, determine whether the set of points (vectors) is a vector space or not. Justify your answer. (a) [x y] satisfying x = 2y (b) [x y] satisfying x = 2y and 2x = y (simultaneously) (c) [x y] satisfying x = 2y + 1 (d) [x y] satisfying xy = 0 2. Determine whether ± ²³´ µ µ · ¸ , ¹ ²³ ´ µ µ · ¸ and
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Unformatted text preview: º ²³ ´ µ µ µ » ¸ are linearly dependent or independent. 3. Find the bases (i.e. the basis vectors) for Column space and Null space of the following matrix. ¼ ²³´ µ µ · ¶ µ · · ½ ¶ » ¶ ¶ ¶ µ » ¾ µµ µ¿ ¶ µµ ¸ What is dim(col(A))? What is dim(null(A))? Express the dependent columns in A as a linear combination of independent columns. (Note: col(A) = Range(A). So use the method we discussed to find Range(A))...
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This note was uploaded on 02/28/2011 for the course AMS 210 taught by Professor Fried during the Spring '08 term at SUNY Stony Brook.

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