Matrices Test -...

The symmetric part of the matrix A= $$\begin{bmatrix}
1 &2  &4 \\
6 & 8 & 2\\
2 & -2 &7
\end{bmatrix}$$.

For a matrix $$A \begin{pmatrix} 1& 0 & 0\\ 2 & 1 & 0\\ 3 & 2 & 1\end{pmatrix}$$, if $$U_{1}, U_{2}$$ and $$U_{3}$$ are $$3\times 1$$ column matrices satisfying $$AU_{1} = \begin{pmatrix}1\\ 0 \\ 0
\end{pmatrix}, AU_{2} \begin{pmatrix}2\\3 \\ 0
\end{pmatrix}, AU_{3} = \begin{pmatrix}2\\ 3\\ 1
\end{pmatrix}$$ and $$U$$ is $$3\times 3$$ matrix whose columns are $$U_{1}, U_{2}$$ and $$U_{3}$$
Then sum of the elements of $$U^{-1}$$ is

If $$A$$ is a scalar matrix $$kI$$ with scalar $$k\ne 0$$ of order $$3$$, the $${A}^{-1}$$ is:

If $$A = \begin{bmatrix} 4& -2\\ 6 & -3\end{bmatrix}$$, then $$A^2$$ is

If $$\bigl(\begin{smallmatrix} 1& 2\\ 2 & 1\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix} x \\ y \end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 2 \\  4 \end{smallmatrix}\bigr)$$, then the values of $$x$$ and $$y$$ respectively, are

If $$A = \bigl(\begin{smallmatrix} 4& -2\\ 6 & -3\end{smallmatrix}\bigr)$$, then $$A^2$$ is

If $$A \times \bigl(\begin{smallmatrix} 1& 1\\0  & 2\end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix}1 & 2 \end{smallmatrix}\bigr)$$, then the order of A is

$$\bigl(\begin{smallmatrix} -1& 0\\ 0 & 1\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix}a & b\\ c & d\end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 1& 0\\ 0 & -1\end{smallmatrix}\bigr)$$, then the values of $$a, b, c $$ and $$d $$ respectively are

If $$\bigl(\begin{smallmatrix}a & 3\\ 1 & 2\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix} 2 \\ -1 \end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 5\\ 0 \end{smallmatrix}\bigr)$$, then the value of $$a$$ is

If $$A=\left[ \begin{matrix} 1 & -2 & 3 \end{matrix} \right] $$ and $$B=\left[ \begin{matrix} -1 \\ 2 \\ -3 \end{matrix} \right] $$, then $$A + B$$ is