Rank of a Matrix

Find the rank of the $\left[\begin{array}{cccc}3& -8& 5& 2\\ 2& -5& 1& 4\\ -1& 2& 3& -2\end{array}\right]$ by row reduction method.

Find the rank of the matrix by minor method: $\left[\begin{array}{ccc}1& -2& 3\\ 2& 4& -6\\ 5& 1& -1\end{array}\right]$

Find the rank of the matrix by minor method: $\left[\begin{array}{cc}2& -4\\ -1& 2\end{array}\right]$.

The rank of the matrix $\left[\begin{array}{cccc}1& 2& 3& 4\\ 2& 4& 6& 8\\ -1& -2& -3& -4\end{array}\right]$ is

Let $a, b\in R-\left\{0\right\}$ and $I_2$ be the identity matrix of order $2$. Then the rank of the (block) matrix $\left[\begin{array}{ll}a{I}_2& b{I}_2\\ a{I}_2& b{I}_2\end{array}\right]$ is

If the matrix $A=\left[\begin{array}{c}\begin{array}{ccc}1& 2& 3\\ 2& 4& 3\\ 3& 2& 1\end{array} \begin{array}{c}0\\ 2\\ 3\end{array}\\ \begin{array}{ccc}6& 8& 7\end{array} \alpha \end{array}\right]$ is of rank $3$ , then $\alpha$ equals to

If the matrix $A=\left[\begin{array}{lll}y+a& b& c\\ a& y+b& c\\ a& b& y+c\end{array}\right]$ has rank $3,$ then -

The rank of  $\left|\begin{array}{c}1 -1 1\\ 1 1 -1\\ -1 1 1\end{array}\right|$ is

If the rank of the matrix $\left[\begin{array}{ccc}-1& 2& 5\\ 2& -4& a-4\\ 1& -2& a+1\end{array}\right]$is $1$, than the value of $a$ is

If $A=\left[\begin{array}{ccc}2& 4& 5\\ 4& 8& 10\\ -6& -12& -15\end{array}\right],$the rank of $A$ is equal to

The rank of the matrix$\left[\begin{array}{ccc}-1& 2& 5\\ 2& -4& a-4\\ 1& -2& a+1\end{array}\right]$is

The rank of matrix$\left[\begin{array}{c}4 1 0 0\\ 3 0 1 0\\ 6 0 2 0\end{array}\right]$is

If the points($x_1,y_1),\left(x_2,y_2\right)$and$(x_3,y_3)$are collinear,

then the rank of the matrix$\left[\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right]$will always be less than

The rank of the matrix$\left[\begin{array}{ccc}4& 2& (1-x)\\ 5& k& 1\\ 6& 3& (1+x)\end{array}\right]$is$2,$then

The rank of the matrix $\left[\begin{array}{ccc}4& 2& \left(1-x\right)\\ 5& k& 1\\ 6& 3& \left(1+x\right)\end{array}\right]$  is  $2$ , then

The rank of the matrix $\text{A}=\left[\begin{array}{cccc}2& 3& 1& 4\\ 0& 1& 2& -1\\ 0& -2& -4& 2\end{array}\right]$  is

For what values of $x$ the matrix $\left[\begin{array}{ccc}3+x& 5& 2\\ 1& 7+x& 6\\ 2& 5& 3+x\end{array}\right]$ has the rank  $2?$ 

Rank of the matrix $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$ is