for the constants c1, C2, ... and cą in the equation c, v,+ c,V2 + .…·+ C4VĄ = V5. From your results of part a, b, c, and d, what is the span of Е. a. vi and v2 b. v1, v2, and v3 с. Т, Q, апd S

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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solve E

10
3
1
V5
-8
4
V1
V2
V3
-2
V4
4
6.
A.
Without calculations, determine if the set of vectors, S = {v1, v2, v3, V4, v5}, is
linearly dependent or independent. S consists of 5 vectors in R*.
В.
Determine whether the set of vectors, T = {v1, v2, V3, V4}, is linearly dependent or
independent using the rank of the matrix composed of the vectors in T.
С.
Determine whether the set of vectors, Q = {v1, v3, V4, V5}, is linearly dependent or
independent using the determinant of the matrix composed of the vectors in Q.
D.
Show that vs can be written as a linear combination of v1, v2, v3 and v4 by solving
for the constants C1, C2, ... and c, in the equation c, v, + C2V2 + …-+ C4V4 = V5.
From your results of part a, b, c, and d, what is the span of
a. vi and v2
b. Vi, V2, and v3
с. Т, Q, аnd S
Е.
Transcribed Image Text:10 3 1 V5 -8 4 V1 V2 V3 -2 V4 4 6. A. Without calculations, determine if the set of vectors, S = {v1, v2, v3, V4, v5}, is linearly dependent or independent. S consists of 5 vectors in R*. В. Determine whether the set of vectors, T = {v1, v2, V3, V4}, is linearly dependent or independent using the rank of the matrix composed of the vectors in T. С. Determine whether the set of vectors, Q = {v1, v3, V4, V5}, is linearly dependent or independent using the determinant of the matrix composed of the vectors in Q. D. Show that vs can be written as a linear combination of v1, v2, v3 and v4 by solving for the constants C1, C2, ... and c, in the equation c, v, + C2V2 + …-+ C4V4 = V5. From your results of part a, b, c, and d, what is the span of a. vi and v2 b. Vi, V2, and v3 с. Т, Q, аnd S Е.
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