Matrices Test -...

If $$A = \begin{vmatrix} 5 & x-2 \\ 2x+3 & x+1 \end{vmatrix}$$ is symmetric, then $$x = $$_____

If $$A=\begin{bmatrix}x&y&z\end{bmatrix},$$ $$ B=\begin{bmatrix}a&h&g\\h&b&f\\g&f&c\end{bmatrix}, C=\begin{bmatrix}\alpha & \beta & \gamma \end{bmatrix}^{T}$$ then $$ABC$$ is

If $$A=\begin{bmatrix} 3 & 3 & 3\\ 3 & 3 & 3\\ 3 & 3 & 3\end{bmatrix}$$, then $$A^3=$$ ___________.

If $$A =\begin{pmatrix} -2& 2\\ 2 & -2\end{pmatrix}$$, then which one of the following is correct?

If A = $$ \begin{bmatrix} \alpha & 0 \\ 1 & 1\end{bmatrix}$$ , B = $$ \begin{bmatrix} 1 & 0 \\ 5 & 1\end{bmatrix}$$ whenever $$A^2 \, = \, B$$
then values of $$\alpha$$ is 

Let A = $$\begin{bmatrix}
              0 & 0 & -1 \\[0.3em]
              0 & -1 & 0 \\[0.3em]
              -1 & 0 & 0
              \end{bmatrix}.$$ Then the only correct statement $$A$$ is

Using elementary row transformation find the inverse of the matrix A = $$\left[\begin {array}{ll} 3 & -1  &  -2\\ 2  &  0  & -1\\ 3 & -5  &  0 \end {array}\right]$$

Given $$A= \begin{bmatrix}  3&6  \\ -2&-8 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 16\end{bmatrix}$$, find the matrix $$X$$ such that $$XA=B$$.

Obtain the inverse of the following matrix using elementary operation:
$$A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$$

If $$I =\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & \quad \quad 0 & \quad 1 \end{pmatrix},$$ $$P=\begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & \quad \quad 0 & \quad -2 \end{pmatrix},$$ then the matrix $$P^3+2P^2$$ is equal to