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Problem. Working in R3, determine whether (-2,2, 2) is a linear combination of (1,2,-1) and (-3,-3.3).

Problem. Working in R3, determine whether (-2,2, 2) is a linear combination of (1,2,-1) and (-3,-3.3).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem. Working in R3, determine whether (-2,2,2) is a linear combination of (1, 2, -1) and (-3,-3.3). Problem 8. Determine whether the 2x2 matrix (19) is in the span of {(18), (11), (18)}. Problem 9. Let S₁ and S₂ be subsets of a vector space V. Prove that span(S₁ S₂) span(S₁) span(S₂). Give an example in which span(S₁ S₂) and span(S₁) n span(S₂) are equal and one in which they are unequal.
Transcribed Image Text:Problem. Working in R3, determine whether (-2,2,2) is a linear combination of (1, 2, -1) and (-3,-3.3). Problem 8. Determine whether the 2x2 matrix (19) is in the span of {(18), (11), (18)}. Problem 9. Let S₁ and S₂ be subsets of a vector space V. Prove that span(S₁ S₂) span(S₁) span(S₂). Give an example in which span(S₁ S₂) and span(S₁) n span(S₂) are equal and one in which they are unequal.
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