Question

In finding the rank of a  3x3 matrix, if the determinant value is not equal to zero then the rank of the matrix is _____________

a.

one

b.

zero

c.

three

d.

two

​

Answer 1

Answer:

1

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

In finding the rank of a  3 × 3 matrix, if the determinant value is not equal to zero then the rank of the matrix is _______

a. one

b. zero

c. three

d. two

EVALUATION

We know that for a non zero matrix A 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 it is given that the given matrix is a  3 × 3 matrix

The determinant value is not equal to zero

Thus the matrix has at least one non-zero minor of order 3

Hence rank of the matrix is 3

FINAL ANSWER

Hence the correct option is c. three

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