Question

if A is non zero matrix of order 3*3 the rank of A is 3 than A is​

Answer 1

SOLUTION

GIVEN

• A is non zero matrix of order 3×3

• The rank of A is 3

TO DETERMINE

The nature of the matrix A

CONCEPT TO BE IMPLEMENTED

RANK OF A MATRIX

Let A be a non zero matrix of order m × n. Then 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

PROPERTIES

1. For a non zero matrix A of order m × n

$\sf{0 < rank \: of \: A \leqslant \: min \{ \: m,n \} }$

2. For a square matrix A of order n

rank of A < n, or = n according as A is singular or non-singular

EVALUATION

A is non zero matrix of order 3×3

A is non zero matrix of order 3×3 The rank of A is 3

So A has one non zero minor of order 3

So by property 2,

the matrix A is non singular

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LEARN MORE FROM BRAINLY

If [1 2 3] B = [34],

then the order of the matrix B is

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