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1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes, since w can't be written as a linear combination of the vectors v1, U2 and v3 . Yes since the equation X1U1 + ×2V2 + X3U3 = w has a solution No since the equation x1vị + ×2U2 + X3U3 = w has no solutions. No since w can be written as a linear combination of the vectors vị, U2 and v3 .

1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes, since w can't be written as a linear combination of the vectors v1, U2 and v3 . Yes since the equation X1U1 + ×2V2 + X3U3 = w has a solution No since the equation x1vị + ×2U2 + X3U3 = w has no solutions. No since w can be written as a linear combination of the vectors vị, U2 and 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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3 6. 3 Let vi U2 = U3 and w = -2 2 Is w in the subspace spanned by {v1, v2 , V3}? Why ? Yes, since w can't be written as a linear combination of the vectors v1, U2 and v3 . Yes since the equation x1vị + X2U2 + X3U3 = w has a solution No since the equation x1Ui + ×2V2 + X3U3 = w has no solutions. O No since w can be written as a linear combination of the vectors U1, U2 and v3 .
Transcribed Image Text:3 6. 3 Let vi U2 = U3 and w = -2 2 Is w in the subspace spanned by {v1, v2 , V3}? Why ? Yes, since w can't be written as a linear combination of the vectors v1, U2 and v3 . Yes since the equation x1vị + X2U2 + X3U3 = w has a solution No since the equation x1Ui + ×2V2 + X3U3 = w has no solutions. O No since w can be written as a linear combination of the vectors U1, U2 and v3 .
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