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Let u, w, v₁, v2, and v3 be the vectors in R defined by -19 37 3 4 -8 -18 12 2 U= 0=0 w= 0= 26 8 u+ 0 V1 = w+ (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. ₁+0 (b) is w E 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. V₁+ V₂ = (c) Type the dimension of span{v1, U2, U3, U}: -10 -19 -17 19 2+0 V3 = V₂+ -8 14 3 V3 V3

Let u, w, v₁, v2, and v3 be the vectors in R defined by -19 37 3 4 -8 -18 12 2 U= 0=0 w= 0= 26 8 u+ 0 V1 = w+ (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. ₁+0 (b) is w E 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. V₁+ V₂ = (c) Type the dimension of span{v1, U2, U3, U}: -10 -19 -17 19 2+0 V3 = V₂+ -8 14 3 V3 V3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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Let u, w, v₁, v2, and v3 be the vectors in R* defined by 37 3 -18 2 u= 19 -4 12 -1 0=0 w= 0 -8 26 8 u+ 0 V1 = w+ -9 v₂ = (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. v₁+ (c) Type the dimension of span{v₁, U2, U3, U}: -10 -19 -17 -19 22+0 V3 = 21+0 (b) Is w E 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+ -8 -8 14 3 V3 V3
Transcribed Image Text:Let u, w, v₁, v2, and v3 be the vectors in R* defined by 37 3 -18 2 u= 19 -4 12 -1 0=0 w= 0 -8 26 8 u+ 0 V1 = w+ -9 v₂ = (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. v₁+ (c) Type the dimension of span{v₁, U2, U3, U}: -10 -19 -17 -19 22+0 V3 = 21+0 (b) Is w E 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+ -8 -8 14 3 V3 V3
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