Let A be an m X n matrix. Answer the following questions with either 'true' or 'false'. he vectors of Rm that are not in C(A), the column space of A, form a subspace of R™. C(A) contains only the zero vector, then A must be the zero matrix; i.e., the matrix in which every entry is the scalar '0'. he column space C(2A) of the matrix 2A is the same as C(A), the column space of of the matrix A.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let A be an m X n matrix. Answer the following questions with either 'true' or 'false'.
(a) The vectors of Rm that are not in C(A), the column space of A, form a subspace of R™.
(b) If C(A) contains only the zero vector, then A must be the zero matrix; i.e., the matrix in which every entry is the scalar '0'.
(c) The column space C(2A) of the matrix 2A is the same as C(A), the column space of of the matrix A.
(a)
(b)
(c)
Transcribed Image Text:Let A be an m X n matrix. Answer the following questions with either 'true' or 'false'. (a) The vectors of Rm that are not in C(A), the column space of A, form a subspace of R™. (b) If C(A) contains only the zero vector, then A must be the zero matrix; i.e., the matrix in which every entry is the scalar '0'. (c) The column space C(2A) of the matrix 2A is the same as C(A), the column space of of the matrix A. (a) (b) (c)
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