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Given an m x n matrix A with rank(A) = r, what is the nullity of A? (a) The dimension of the nullspace of A is n since nullity (A) equals the number of columns. (b) The dimension of the nullspace of A is m since nullity(A) equals the number of rows. (c) The dimension of the nullspace of A is r since nullity(A) = rank(A). (d) The dimension of the nullspace of A is n - r since nullity (A) = n - rank(A). (e) The dimension of the nullspace of A is 0 since Ax=0 only has the trivial solution, for any A.

Given an m x n matrix A with rank(A) = r, what is the nullity of A? (a) The dimension of the nullspace of A is n since nullity (A) equals the number of columns. (b) The dimension of the nullspace of A is m since nullity(A) equals the number of rows. (c) The dimension of the nullspace of A is r since nullity(A) = rank(A). (d) The dimension of the nullspace of A is n - r since nullity (A) = n - rank(A). (e) The dimension of the nullspace of A is 0 since Ax=0 only has the trivial solution, for any 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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Given an m x n matrix A with rank(A) = r, what is the nullity of A? (a) The dimension of the nullspace of A is n since nullity(A) equals the number of columns. (b) The dimension of the nullspace of A is m since nullity(A) equals the number of rows. (c) The dimension of the nullspace of A is r since nullity(A) = rank(A). (d) The dimension of the nullspace of A is n - r since nullity (A) = n- rank(A). (e) The dimension of the nullspace of A is 0 since Ax=0 only has the trivial solution, for any A.
Transcribed Image Text:Given an m x n matrix A with rank(A) = r, what is the nullity of A? (a) The dimension of the nullspace of A is n since nullity(A) equals the number of columns. (b) The dimension of the nullspace of A is m since nullity(A) equals the number of rows. (c) The dimension of the nullspace of A is r since nullity(A) = rank(A). (d) The dimension of the nullspace of A is n - r since nullity (A) = n- rank(A). (e) The dimension of the nullspace of A is 0 since Ax=0 only has the trivial solution, for any A.
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