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True of False Choose True if the statement is correct, otherwise False. 1. Suppose a matrix A has three rows, then adding a negative multiple of Row 1 to Row 2 doesn't change the determinant. 2. For any matrix A of entry ajk transposed to AT, the entry at akj, where j = k remains unchanged. 3. Matrix A and matrix B cannot be added if their dimensions are not the same. 4. If det(A) is the same as det(B), it is safe to say that matrix A = matrix B. 5. Suppose A is a 3 x 5 matrix and B is a 5 x 8 matrix, then (AB)T is a 3 x 8 matrix.

True of False Choose True if the statement is correct, otherwise False. 1. Suppose a matrix A has three rows, then adding a negative multiple of Row 1 to Row 2 doesn't change the determinant. 2. For any matrix A of entry ajk transposed to AT, the entry at akj, where j = k remains unchanged. 3. Matrix A and matrix B cannot be added if their dimensions are not the same. 4. If det(A) is the same as det(B), it is safe to say that matrix A = matrix B. 5. Suppose A is a 3 x 5 matrix and B is a 5 x 8 matrix, then (AB)T is a 3 x 8 matrix.

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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True of False: Choose True if the statement is correct, otherwise False.

True of False Choose True if the statement is correct, otherwise False. 1. Suppose a matrix A has three rows, then adding a negative multiple of Row 1 to Row 2 doesn't change the determinant. 2. For any matrix A of entry ajk transposed to AT, the entry at akj, where j = k remains unchanged. 3. Matrix A and matrix B cannot be added if their dimensions are not the same. 4. If det(A) is the same as det(B), it is safe to say that matrix A = matrix B. 5. Suppose A is a 3 x 5 matrix and B is a 5 x 8 matrix, then (AB)T is a 3 x 8 matrix.
Transcribed Image Text:True of False Choose True if the statement is correct, otherwise False. 1. Suppose a matrix A has three rows, then adding a negative multiple of Row 1 to Row 2 doesn't change the determinant. 2. For any matrix A of entry ajk transposed to AT, the entry at akj, where j = k remains unchanged. 3. Matrix A and matrix B cannot be added if their dimensions are not the same. 4. If det(A) is the same as det(B), it is safe to say that matrix A = matrix B. 5. Suppose A is a 3 x 5 matrix and B is a 5 x 8 matrix, then (AB)T is a 3 x 8 matrix.
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