3 1 V1 V3 V4 V5 -2 4 6. 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*. Determine whether the set of vectors, T = {v1, V2, V3, v4}, is linearly dependent or А. В. %3D independent using the rank of the matrix composed of the vectors in T. 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. С. Show that v5 can be written as a linear combination of v1, v2, V3 and v4 by solving for the constants c,, 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 апd S Е.

3 1 V1 V3 V4 V5 -2 4 6. 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*. Determine whether the set of vectors, T = {v1, V2, V3, v4}, is linearly dependent or А. В. %3D independent using the rank of the matrix composed of the vectors in T. 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. С. Show that v5 can be written as a linear combination of v1, v2, V3 and v4 by solving for the constants c,, 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 апd S Е.

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

100%

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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