Recent questions tagged matrix-algebra

Let $A=\left(\begin{array}{ccc}1 & 0 & 1 \\ 0 & k & 0 \\ 3 & 0 & -1\end{array}\right)$. If the eigenvalues of $A$ are $-2,1$, and $2$ , then the value of $k$ is $\_\_\_\_...

If the eigenvalues of a $2 \times 2$ matrix $P$ are $4$ and $2,$ then the eigenvalues of the matrix $P^{-1}$ are$0, 0$$0.0625, 0.25$$0.25, 0.5$$2, 4$

A $2\times 2$ matrix $\textbf{P}$ has an eigen value $\lambda_{1}=2$ with eigenvector $x_{1}=\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ and another eigenvalue $\lambda_{2}=5...

If $A = \begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}$, then $A^2+3A$ will be$\begin{bmatrix} 30 & 20 \\ 10 & 20 \end{bmatrix} \\$$\begin{bmatrix} 28 & 10 \\ 4 & 18 \end{b...

If $P=\begin{bmatrix}1&1\\2&2\end{bmatrix}, Q=\begin{bmatrix}2&1\\2&2\end{bmatrix}$ and $R=\begin{bmatrix}3&0\\1&3\end{bmatrix}$, which one of the following statements is...