Question

Find the rank if A= [1 5 6] [2 3 4]
[1 2 2]​

Answer 1

Answer:

first=234

sceond=156

third=122

Answer 2

Rank of a matrix is the order of largest submatrix whose determinant is not zero.

Given Matrix A,

$A = \bigg( \: \: \begin{matrix} 1&5&6 \\ 2&3& 4\\ 1&2&2\\ \end{matrix} \: \: \bigg)$

Now DetA,

$|A| = \: \: \begin{vmatrix} 1&5&6 \\ 2&3& 4\\ 1&2&2\\ \end{vmatrix} \: \: \\ \\ |A | = 1(3 \times 2 - 4 \times 2) - 5(2 \times 2 - 4 \times 1) + 6(2 \times 2 - 3 \times 1) \\ \\ |A | = 1(6 - 8) - 5(0) + 6(4 - 3) \\ \\ |A | = - 2 + 6 = 4$

Since, DetA didn't vanish, The rank of the matrix A is the order of determinant A.

Therefore, The rank of A is 3.