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3. For each of the following statements, indicate if it is true (T) or false (F). The set is linearly independent. For any given 2 x 2 matrices A, B and C such that A # 02x2, if AB = AC then we necessarily have B = C. If the columns of a 4 x 4 matrix A are linearly independent, then the linear system Ax = 0 has no solutions other than the trivial solution. For any two 3 x 3 matrices A and B, we have (AT B")" = AB.

3. For each of the following statements, indicate if it is true (T) or false (F). The set is linearly independent. For any given 2 x 2 matrices A, B and C such that A # 02x2, if AB = AC then we necessarily have B = C. If the columns of a 4 x 4 matrix A are linearly independent, then the linear system Ax = 0 has no solutions other than the trivial solution. For any two 3 x 3 matrices A and B, we have (AT B")" = AB.

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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3. For each of the following statements, indicate if it is true (T) or false (F). The set is linearly independent. For any given 2 x 2 matrices A, B and C such that A 02x2, if AB = AC then we necessarily have B = C. If the columns of a 4 x 4 matrix A are linearly independent, then the linear system Ax = 0 has no solutions other than the trivial solution. For any two 3 x 3 matrices A and B, we have (AT B")" = AB.
Transcribed Image Text:3. For each of the following statements, indicate if it is true (T) or false (F). The set is linearly independent. For any given 2 x 2 matrices A, B and C such that A 02x2, if AB = AC then we necessarily have B = C. If the columns of a 4 x 4 matrix A are linearly independent, then the linear system Ax = 0 has no solutions other than the trivial solution. For any two 3 x 3 matrices A and B, we have (AT B")" = AB.
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