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Consider the following matrix A and its reduced row-echelon form: 3 -3 12 -6 -27 -24 1 -1 4 -2 -9 -8 3 6 -24 -15 18 21 -1 0 0 3 4 3 A = rref(A) = Basis for row(A). 1 0 0 -3 -4 -3 0 1-4 -1 5 5 000 0 0 0 0000 0 0 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 1 Jal

Consider the following matrix A and its reduced row-echelon form: 3 -3 12 -6 -27 -24 1 -1 4 -2 -9 -8 3 6 -24 -15 18 21 -1 0 0 3 4 3 A = rref(A) = Basis for row(A). 1 0 0 -3 -4 -3 0 1-4 -1 5 5 000 0 0 0 0000 0 0 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 1 Jal

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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Consider the following matrix A and its reduced row-echelon form: -3 12 -6 -27 -24 -2 -9 -8 −1 4 3 6 -24 -15 18 21 -1 0 0 3 4 3 A = 3 0 H 0 Dimension of null(A): 1 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 1 Basis for row(A): Basis for null(A): 0 0 0 Dimension of col(A): 1 {}} Basis for col(A): rref(A) = 1 0 0 −3 −4 −3 01 -4 -1 5 5 000 0 00 000 0 0 0
Transcribed Image Text:Consider the following matrix A and its reduced row-echelon form: -3 12 -6 -27 -24 -2 -9 -8 −1 4 3 6 -24 -15 18 21 -1 0 0 3 4 3 A = 3 0 H 0 Dimension of null(A): 1 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 1 Basis for row(A): Basis for null(A): 0 0 0 Dimension of col(A): 1 {}} Basis for col(A): rref(A) = 1 0 0 −3 −4 −3 01 -4 -1 5 5 000 0 00 000 0 0 0
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