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
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Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e5b1a56-3032-449a-acc6-d2196fb84e38%2F7b4c7514-b317-416b-a307-50e18050fd34%2Fbilua3j_processed.png&w=3840&q=75)
Transcribed Image Text: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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