Question

if a square matrix of order n with rank r with r=n then matrix A is​

Answer 1

$\sf { \underline{SOLUTION}}$

GIVEN

A is a square matrix of order n with rank r with r = n

TO DETERMINE

Type of matrix A is

CONCEPT TO BE IMPLEMENTED

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

EVALUATION

Here it is given that A is a square matrix of order n with rank r with r = n

∵ rank of A = order of A

∴ A is non-singular

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