The Brainliest Answer!

This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Rank of a square matrix is found by finding the determinant. If the determinant is non-zero, the dimension of the square matrix is the rank.

If the determinant of A of size n x n is zero, then it is possible that there are two identical rows or columns. Or, algebraic sum of some rows or columns is equal to a row or column. Then the rank cannot be n.

We remove one of the identical rows or columns and then find the determinant of n-1 x n-1 matrix. If its determinant is non zero, then n-1 will be the rank of the matrix A.

Determinant is found by the usual method.

det|  \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] | = det | \left[\begin{array}{ccc}1&2&3\\4-1&5-2&6-3\\7-1&8-2&9-3\end{array}\right] | \\ \\ \\ = det| \left[\begin{array}{ccc}1&2&3\\3&3&3\\6&6&6\end{array}\right] | = 0 \\ \\
Determinant is zero because 3nd row is a multiple of 2nd row.

Let us remove the third row and column. and find the determinant again of the 2x2 matrix.

det|  \left[\begin{array}{ccc}1&2\\4&5\end{array}\right] | = 1*5 - 4*2 = -3  \neq 0. \\ \\ So\ Rank = 2.\\

1 5 1
power supply gone. i continue ans
oo k
u seem to know it. then why ask a question?
select as best answer.
ok see u.