Find the rank of matrix

$\begin{bmatrix}1&2&3\\1&4&2\\2&6&5\end{bmatrix}$

Find the rank of matrix

$\begin{bmatrix}2&3&4&-1\\5&2&0&-1\\-4&5&12&-1\end{bmatrix}$

Find the rank of matrix

$\begin{bmatrix}1&2&3&0\\2&4&3&2\\3&2&1&3\\6&8&7&5\end{bmatrix}$

Reduce each of the following matrix to normal form and hence find their rank

$\begin{bmatrix}2&3&-1&-1\\1&-1&-2&-4\\3&1&3&-2\\6&3&0&-7\end{bmatrix}$

Find the rank of matrix

$\begin{bmatrix}8&1&3&6\\0&3&2&2\\-8&-1&-3&4\end{bmatrix}$

For the matrix 

$A=\begin{bmatrix}1&1&2\\1&2&3\\0&-1&-1\end{bmatrix}$

For non singular matrices P and Q such that PAQ is in the normal form. Hence find the rank of A.

Reduce to triangular form

$\begin{bmatrix}3&-4&-5\\-9&1&4\\-5&3&1\end{bmatrix}$

Use Gauss-jordan method to find the inverse of matrix$\begin{bmatrix}8&4&3\\2&1&1\\1&2&1\end{bmatrix}$

Solve thehelp of matrix the simultaneous equations :

$x+y+z=3, x+2y+3z=4, x+4y+9z=6$

Solve the system of equations

$2x_{1}+x_{2}+2x_{3}+x_{4}=6$

$4x_{1}+3x_{2}+3x_{3}-3x_{4}=-1$

$6x_{1}-6x_{2}+6x_{3}+12x_{4}=36$

$2x_{1}+2x_{2}-x_{3}+x_{4}=10$

Using matrix mathod , show that the equations

3x+3y+2z=1,

x+2y=4,

10y+3z=-2,

2x-3y-z=5

are consistent and hence obtain the solution for x,y,and z.