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(1 2 3 3 2 4 1 3 2 Let A = 1 2 -4 -3 -5 3 6 3 6 1 (i) basis are the rows in A. Find a basis for the row space of A such that the vectors in the (ii) Show how you obtain your answer. Extend the basis in (i) to a basis for R% with some standard basis vectors. -000 3 (iii) Let S = Show that S is a basis for 6. 6 the column space of A.

(1 2 3 3 2 4 1 3 2 Let A = 1 2 -4 -3 -5 3 6 3 6 1 (i) basis are the rows in A. Find a basis for the row space of A such that the vectors in the (ii) Show how you obtain your answer. Extend the basis in (i) to a basis for R% with some standard basis vectors. -000 3 (iii) Let S = Show that S is a basis for 6. 6 the column space of A.

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 2 3 3 2 4 1 3 Let A = 1 2 -4 -3 -5 3 6 3 1 (i) basis are the rows in A. Find a basis for the row space of A such that the vectors in the Extend the basis in (i) to a basis for R with some standard basis vectors. (ii) Show how you obtain your answer. 1000 3 3 4 3 (ii) Let S = Show that S is a basis for 2 -3 6 6 the column space of A. Is it possible to find a matrix in row echelon form whose column (iv) space is the same as that of A? Justify your answer.
Transcribed Image Text:1 2 3 3 2 4 1 3 Let A = 1 2 -4 -3 -5 3 6 3 1 (i) basis are the rows in A. Find a basis for the row space of A such that the vectors in the Extend the basis in (i) to a basis for R with some standard basis vectors. (ii) Show how you obtain your answer. 1000 3 3 4 3 (ii) Let S = Show that S is a basis for 2 -3 6 6 the column space of A. Is it possible to find a matrix in row echelon form whose column (iv) space is the same as that of A? Justify your answer.
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