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-1 −3 −7 −2 304 -5-4 1 -4 -3 3 32 22 -2 -1 -3-7-2 1 0 -5 -4 1 4. Consider A = = with a corresponding A = = 3 4 1 -4-3 3 4 3 32 22 -2 -4 • State a basis for the column space of A. • Choose one of the columns from A not selected as part of the basis and show how it is a linear combination of your basis. 5. Using the same matrix A as in the previous problem: • State a basis for the null space (kernel) of A. • Give an example of a nonzero vector in the null space that is not one of your basis vectors.

-1 −3 −7 −2 304 -5-4 1 -4 -3 3 32 22 -2 -1 -3-7-2 1 0 -5 -4 1 4. Consider A = = with a corresponding A = = 3 4 1 -4-3 3 4 3 32 22 -2 -4 • State a basis for the column space of A. • Choose one of the columns from A not selected as part of the basis and show how it is a linear combination of your basis. 5. Using the same matrix A as in the previous problem: • State a basis for the null space (kernel) of A. • Give an example of a nonzero vector in the null space that is not one of your basis vectors.

Advanced Engineering Mathematics
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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-1 −3 −7 −2 304 -5-4 1 -4 -3 3 32 22 -2 -1 -3-7-2 1 0 -5 -4 1 4. Consider A = = with a corresponding A = = 3 4 1 -4-3 3 4 3 32 22 -2 -4 • State a basis for the column space of A. • Choose one of the columns from A not selected as part of the basis and show how it is a linear combination of your basis. 5. Using the same matrix A as in the previous problem: • State a basis for the null space (kernel) of A. • Give an example of a nonzero vector in the null space that is not one of your basis vectors.
Transcribed Image Text:-1 −3 −7 −2 304 -5-4 1 -4 -3 3 32 22 -2 -1 -3-7-2 1 0 -5 -4 1 4. Consider A = = with a corresponding A = = 3 4 1 -4-3 3 4 3 32 22 -2 -4 • State a basis for the column space of A. • Choose one of the columns from A not selected as part of the basis and show how it is a linear combination of your basis. 5. Using the same matrix A as in the previous problem: • State a basis for the null space (kernel) of A. • Give an example of a nonzero vector in the null space that is not one of your basis vectors.
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