47. Let A be an arbitrary 2 × 2 matrix, and B an invertible 2 × 2-matrix. Which of the following is NOT always true? (a) The row space of BA is equal to the row space of A. (b) The row space of AB is contained in the row space of B. (c) The column space of AB is equal to the column space of A. (d) The column space of BA is contained in the column space of A.
47. Let A be an arbitrary 2 × 2 matrix, and B an invertible 2 × 2-matrix. Which of the following is NOT always true? (a) The row space of BA is equal to the row space of A. (b) The row space of AB is contained in the row space of B. (c) The column space of AB is equal to the column space of A. (d) The column space of BA is contained in the column space of A.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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
Transcribed Image Text:47. Let A be an arbitrary 2 × 2 matrix, and B an invertible 2 × 2-matrix. Which of the
following is NOT always true?
(a) The row space of BA is equal to the row space of A.
(b) The row space of AB is contained in the row space of B.
(c) The column space of AB is equal to the column space of A.
(d) The column space of BA is contained in the column space of A.
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