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Let u, w, v1, v2, and v3 be the vectors in R4 defined by 1 2 6 25 19 -13 20 17 15 16 -17 -12 11 10 5 12 -8-8-8-8-8 (a) Is u € span{v1, v2, v3}? Write all zeros if it is not in the span or write zero as a non- trivial (not all zero coefficients) linear combination of u, v1, v2, and v3 if u is in the span. 0 = Pu+ Vi+ V3 V2+ (b) Is w span{v1, v2, v3}? Write all zeros if it is not or if it is in the span write zero as a non-trivial (not all zero coefficients) linear combination of w, v1, v2, and v3 if w is in the span. 0 w+ vi+ PV2+ (c) Type the dimension of span{v1, v2, v3, u}: 9. V3

Let u, w, v1, v2, and v3 be the vectors in R4 defined by 1 2 6 25 19 -13 20 17 15 16 -17 -12 11 10 5 12 -8-8-8-8-8 (a) Is u € span{v1, v2, v3}? Write all zeros if it is not in the span or write zero as a non- trivial (not all zero coefficients) linear combination of u, v1, v2, and v3 if u is in the span. 0 = Pu+ Vi+ V3 V2+ (b) Is w span{v1, v2, v3}? Write all zeros if it is not or if it is in the span write zero as a non-trivial (not all zero coefficients) linear combination of w, v1, v2, and v3 if w is in the span. 0 w+ vi+ PV2+ (c) Type the dimension of span{v1, v2, v3, u}: 9. V3

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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Let u, w, v1, v2, and v3 be the vectors in R4 defined by 2 1 17 16 0 6 25 15 -17 -7 u = ข 01 V2 V3 19 -18 -13 20 -12 11 10 -5 -13 12 (a) Is u span{v1, v2, v3}? Write all zeros if it is not in the span or write zero as a non- trivial (not all zero coefficients) linear combination of u, v1, v2, and v3 if u is in the span. 0 u+ V₁+ V3 v2+ (b) Is w span{v1, v2, v3}? Write all zeros if it is not or if it is in the span write zero as a non-trivial (not all zero coefficients) linear combination of w, v1, v2, and v3 if w is in the span. v2+ 0 = w+ (c) Type the dimension of span{v1, v2, v3, u}: Vi+ V3
Transcribed Image Text:Let u, w, v1, v2, and v3 be the vectors in R4 defined by 2 1 17 16 0 6 25 15 -17 -7 u = ข 01 V2 V3 19 -18 -13 20 -12 11 10 -5 -13 12 (a) Is u span{v1, v2, v3}? Write all zeros if it is not in the span or write zero as a non- trivial (not all zero coefficients) linear combination of u, v1, v2, and v3 if u is in the span. 0 u+ V₁+ V3 v2+ (b) Is w span{v1, v2, v3}? Write all zeros if it is not or if it is in the span write zero as a non-trivial (not all zero coefficients) linear combination of w, v1, v2, and v3 if w is in the span. v2+ 0 = w+ (c) Type the dimension of span{v1, v2, v3, u}: Vi+ V3
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