1. Given the following matrix:-1A = 4-12-42-4-6-2A. Determine rref(A).B. Is the vectorb2in the nullspace of A? Why or why not?C. Is the vectorC =in the column space of A? Why or why not?D. Determine the greatest number of independent vectors among v,, V2, V3, and v,, where v, isthe vector equal to the nth column of A.2. Given the following matrix:A =| 1 2 0-3 5 21A. Determine the eigenvalues and eigenvectors of A. The third element of each eigenvector

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1. Given the following matrix: 2 -1 4 -4 -4 -12 A 2 -6 -2 A. Determine rref(A). B. Is the vector b in the nullspace of A? Why or why not? C. Is the vector -3 in the column space of A? Why or why not? D. Determine the greatest number of independent vectors among vị, v2, V3, and V4, where v,

1. Given the following matrix: 2 -1 4 -4 -4 -12 A 2 -6 -2 A. Determine rref(A). B. Is the vector b in the nullspace of A? Why or why not? C. Is the vector -3 in the column space of A? Why or why not? D. Determine the greatest number of independent vectors among vị, v2, V3, and V4, where v,

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 42EQ

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Question

1. Given the following matrix:
-1
A = 4
-12
-4
2
-4
-6
-2
A. Determine rref(A).
B. Is the vector
b
2
in the nullspace of A? Why or why not?
C. Is the vector
C =
in the column space of A? Why or why not?
D. Determine the greatest number of independent vectors among v,, V2, V3, and v,, where v, is
the vector equal to the nth column of A.
2. Given the following matrix:
A =| 1 2 0
-3 5 21
A. Determine the eigenvalues and eigenvectors of A. The third element of each eigenvector

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