TRUE OR FALSE In each case, explain or prove your answer. If A is an m × n matrix, then A and AT have the same rank.
TRUE OR FALSE In each case, explain or prove your answer. If A is an m × n matrix, then A and AT have the same rank.
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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Question
TRUE OR FALSE In each case, explain or prove your answer. If A is an m × n matrix, then A and AT have the
same rank.
Expert Solution
Step 1
If A is an matrix then, the number of rows of A is m and the number of columns of the matrix A
is n.
We know that the transpose of the matrix A is written as . Clearly, if A is an matrix then,
is an matrix.
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