plz provide handwritten answer for q2 part c and d only asap Q2.Consider the vectors:Vi = (2,0,0, - 2),V2 = (-14,-7,-12,54),V3 = (0, 1, 1 -6)V4 = (-32,-15,–25,118).a) Find the dimension of the vector subspace A = < v1,V2,V3,V4>b) Calculate the value of k that makes the vector (-4,k,-2,16)part of this vector subspace.c) Let us now consider the vector subspace B= Calculate the coordinates of thevector V5 = (18,6,6-54in the base B.d) Finally, consider V6 = (-14,-6,-6,a). What must be the value of a for V1, V3i Voto bethree linearly independent vectors?

Answered: Image /qna-images/answer/7b4c7514-b317-416b-a307-50e18050fd34.jpg

c) Let us now consider the vector subspace B= Calculate the coordinates of the vector V5 = (18,6,6-54)in the base B. d) Finally, consider V6 = (-14,-6,-6,a). What must be the value of a for V1, V3i V6to be three linearly independent vectors?

c) Let us now consider the vector subspace B= Calculate the coordinates of the vector V5 = (18,6,6-54)in the base B. d) Finally, consider V6 = (-14,-6,-6,a). What must be the value of a for V1, V3i V6to be three linearly independent vectors?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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plz provide handwritten answer for q2 part c and d only asap

Q2.
Consider the vectors:
Vi = (2,0,0, - 2),
V2 = (-14,-7,-12,54),
V3 = (0, 1, 1 -6)
V4 = (-32,-15,–25,118).
a) Find the dimension of the vector subspace A = < v1,V2,V3,V4>
b) Calculate the value of k that makes the vector (-4,k,-2,16)part of this vector subspace.
c) Let us now consider the vector subspace B= <V1,V3 > Calculate the coordinates of the
vector V5 = (18,6,6-54in the base B.
d) Finally, consider V6 = (-14,-6,-6,a). What must be the value of a for V1, V3i Voto be
three linearly independent vectors?

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