Prove that the rank of transpose of a matrix is same as that of the original matrix
Answers
SOLUTION
TO PROVE
The rank of transpose of a matrix is same as that of the original matrix
PROOF
Let A be a non zero matrix of order m × n. The Rank of A is defined to be the greatest positive integer r such that A has at least one non-zero minor of order r
For a non-zero m × n matrix A
0 < rank of A ≤ min {m, n}
For a non-zero matrix A of order n,
rank of A < , or = n according as A is singular or non-singular
Hence the rank of transpose of a matrix is same as that of the original matrix
Hence the proof follows
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Answer:
show that the rank of the transpose of a matrix is the same as that if the original matrix