Recent questions and answers in Linear Algebra

If $2 X+\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]=\left[\begin{array}{ll}3 & 8 \\ 7 & 2\end{array}\right]$, then $X$ is $\_\_\_\_$.$\left[\begin{array}{ll}2...

Consider the matrix $A=\left[\begin{array}{ccc}2 & 2 & 3 \\ 2 & 5 & 6 \\ 3 & 4 & 10\end{array}\right]$.Which ONE of the following options CORRECTLY lists the eigenvalues ...

A system of linear equations is given as $\mathrm{A X}=\mathrm{B}$, where $\mathrm{A}=\left[\begin{array}{cc}2 & 5 \\ 5 & -2\end{array}\right], \quad \mathrm{B}=\left[\be...

The following is a system of linear equations$$\begin{array}{c} x-2 y+z=34 \\ 2 x+y+z=102 \\x+y-3 z=17\end{array}$$The value of $(x+y+z)$ is $\_\_\_\_\_\_$ (rounded off t...

If $\mathbf{X}$ is a vector, and $\mathbf{A}$ and $\mathbf{B}$ are linear operators; then the correct mathematical relationship(s) is/are$(\mathbf{A}+\mathbf{B}) \mathbf{...

The eigen values of the matrix $\left[\begin{array}{ll}4 & 3 \\ 3 & 4\end{array}\right]$ are$1$$2$$7$$4$

$\mathbf{P}$ and $\mathbf{Q}$ are square matrices. Consider the following$\mathrm{X}:\left(\mathbf{P}^{-\mathbf{1}}\right)^{-1}=\mathbf{P}$Y: Symmetric if $\mathbf{Q}=-\m...

Consider two matrices $\mathbf{P}=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]$ and $\mathbf{Q}=\left[\begin{array}{ll}5 & 4 \\ 0 & 2\end{array}\right]$. If $\...

Given $\mathbf{P}$ is $m \times n$ matrix, $\mathbf{Q}$ is $n \times l$ matrix, $\mathbf{R}$ and $\mathbf{S}$ are $n \times n$ matrices, and superscript $\mathrm{T}$ deno...

Eigen values of the matrix $\left[\begin{array}{cc}0 & 1 \\ -2 & 3\end{array}\right]$ are$1$ and $2$$1$ and $3$$1$ and $-2$$0$ and $3$