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# assign1 - R n . Prove that every ~x ∈ R n can be written...

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Math 136 Assignment 1 Due: Wednesday, Jan 11th 1. Compute the following linear combinations. (a) 1 2 ± 2 6 ² + 1 3 ± 4 3 ² (b) 2 3 ± 3 1 ² - 2 ± 1 / 4 1 / 3 ² (c) 2 ± 2 3 ² + 3 ± 1 6 ² 2. Describe geometrically the following sets and write a simpliﬁed vector equation for each. (a) span ³± 1 - 1 ² , ± - 2 2 ² , ± 0 0 ²´ (b) span 2 - 3 1 , 1 3 0 3. Determine whether 0 - 2 - 2 is in the span of 1 - 1 1 , 2 - 1 3 , 1 1 1 . 4. Assume that B = { ~v 1 ,...,~v k } is a linearly independent set which spans
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Unformatted text preview: R n . Prove that every ~x ∈ R n can be written as a unique linear combination of the vectors in B . 5. Prove that if { ~v 1 ,...,~v k } is linearly independent, then { ~v 1 ,...,~v k-1 } is linearly inde-pendent. 6. Prove that if { ~a, ~ b } is a spanning set for R 2 , then { ~a, ~ b-t~a } is also a spanning set for R 2 for any t ∈ R . 1...
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## This note was uploaded on 02/22/2012 for the course MATH cs136 taught by Professor Mark during the Winter '12 term at Waterloo.

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