Question

A square matrix of order 3 with a non-zero determinant has rank ​

Answer 1

Answer:

You can see that the determinants of each 3 x 3 sub matrices are equal to zero, which show that the rank of the matrix is not 3. Hence, the rank of the matrix B = 2, which is the order of the largest square sub-matrix with a non zero determinant.

Step-by-step explanation:

Answer 2

SOLUTION

TO DETERMINE

A square matrix of order 3 with a non-zero determinant has rank

EVALUATION

Before we evaluate the question we first take a look on rank of a matrix

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

Now we evaluate the question

Let M be the given square matrix of order 3

Since M has a non-zero determinant

So M has one non-zero minor of order 3

Hence rank of the matrix = 3

FINAL ANSWER

A square matrix of order 3 with a non-zero determinant has rank 3

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