Consider the vectors: V1 = (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 =
Consider the vectors: V1 = (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 =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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plz provide answer for part a
![2.
Consider the vectors:
V1 = (2,0,0,-2),
|V2 = (– 14,–7,-12,54),
V3 = (0,1,1-6)
%3D
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,-54)in the base B.
d) Finally, consider V6 = (-14,-6,-6, a). What must be the value of a for Vi, V3i V6to be three
linearly independent vectors?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e5b1a56-3032-449a-acc6-d2196fb84e38%2Fd90a1208-0e38-4ea0-b537-c5d79449cc9f%2F198085t_processed.png&w=3840&q=75)
Transcribed Image Text:2.
Consider the vectors:
V1 = (2,0,0,-2),
|V2 = (– 14,–7,-12,54),
V3 = (0,1,1-6)
%3D
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,-54)in the base B.
d) Finally, consider V6 = (-14,-6,-6, a). What must be the value of a for Vi, V3i V6to be three
linearly independent vectors?
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