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Given an m x n matrix A with rank(A) = r, what is the dimension of the column space of A? (a) The dimension of the column space is m since the columns of A are in Rm. (b) The dimension of the column space is n since dim(col A)) equals the number of columns. (c) The dimension of the column space is r since dim(col A)) = rank(A). (d) The dimension of the column space is n - r since dim(col A) = n - rank(A). (e) The dimension of the column space is nr since A has n columns.

Given an m x n matrix A with rank(A) = r, what is the dimension of the column space of A? (a) The dimension of the column space is m since the columns of A are in Rm. (b) The dimension of the column space is n since dim(col A)) equals the number of columns. (c) The dimension of the column space is r since dim(col A)) = rank(A). (d) The dimension of the column space is n - r since dim(col A) = n - rank(A). (e) The dimension of the column space is nr since A has n columns.

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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Given an m x n matrix A with rank(A) = r, what is the dimension of the column space of A? (a) The dimension of the column space is m since the columns of A are in Rm. (b) The dimension of the column space is n since dim(col A)) equals the number of columns. (c) The dimension of the column space is r since dim(col A)) = rank(A). (d) The dimension of the column space is n - r since dim(col A) = n - rank(A). (e) The dimension of the column space is nr since A has n columns.
Transcribed Image Text:Given an m x n matrix A with rank(A) = r, what is the dimension of the column space of A? (a) The dimension of the column space is m since the columns of A are in Rm. (b) The dimension of the column space is n since dim(col A)) equals the number of columns. (c) The dimension of the column space is r since dim(col A)) = rank(A). (d) The dimension of the column space is n - r since dim(col A) = n - rank(A). (e) The dimension of the column space is nr since A has n columns.
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