Recent questions and answers in Linear Algebra

Given matrix $A = \begin{bmatrix} x & 1 & 3\\ y & 2 & 6\\ 3 & 5 & 7 \end{bmatrix}$, the ordered pair $(x, y)$ for which $\text{det}(A) = 0 $ is$(1, 1)$$(1, 2)$$(2, 2)$$(2...

$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$. $$\textbf{A} = \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \end{bmatrix} \\ \textbf{B} = \begin{bmatrix}b_1 & b_2...

Consider the following $(2\times2)$ matrix $\left( \begin{array}{c} 4 & 0 \\ 0 & 4 \end{array} \right)$Whi...

For the matrix $\begin{pmatrix} 4 & 3\\ 3& 4 \end{pmatrix}$, if $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ is an eigenvector, the corresponding eigenvalue is __________ .

Which one of the following is the pair of eigenvalues of the matrix $\left[\begin{array}{cc}-3 & 4 \\ 4 & 3\end{array}\right]?$$-7,7$$-5,5$$-4,3$$-3,4$

A system of $n$ homogeneous linear equations containing $n$ unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is$1$$-1$$0$...

For the matrix $A=\begin{bmatrix} \cos\theta &-\sin\theta \\ \sin \theta & \cos\theta \end{bmatrix}$ if $\det$ stands for the determinant and $A^{T}$ is the transpose of ...

If a matrix $M$ is defined as $M=\left[\begin{array}{cc}10 & 6 \\ 6 & 10\end{array}\right]$, the sum of all the eigenvalues of $M^3$ is equal to______________(in integer)...

Consider the matrix$$A=\left[\begin{array}{ll} 2 & 3 \\ 1 & 2\end{array}\right]$$The eigenvalues of the matrix are $0.27$ and $\_\_\_\_$ (rounded off to $2$ decimal place...