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Homework 6
(Due Monday, December 6, 2010)
1.
Each of the following gives you a set of points (vectors in xy 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
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µ
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,
¹
²³ ´
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µ
µ
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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.
 Spring '08
 FRIED

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