Questions without answers in Linear Algebra

​​​​Consider a Cartesian coordinate system defined over a $3$-dimensional vector space with orthogonal unit basis vectors $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$. Let ...

​​​​​​Consider a linear homogeneous system of equations $\text{Ax}=0$, where $\text{A}$ is an $n \times n$ matrix, $\text{x}$ is an $n \times 1$ vector and $0$ is an $n \...

Consider a matrix $\text{A}=\left[\begin{array}{cc}-5 & a \\ -2 & -2\end{array}\right]$, where $a$ is a constant. If the eigenvalues of $\text{A}$ are $-1$ and $-6$, then...

Let $A$ be a square matrix of size $n \times n (n>1)$. The elements of $A=\{a_{ij}\}$ are given by $$a_{ij} = \begin{cases} i \times j, & \text{if } i \geq j \\ 0, & \tex...

Sum of the eigenvalues of the matrix $\begin{bmatrix} 2 & 4 & 6 \\ 3 & 5 & 9 \\ 12 & 1 & 7 \end{bmatrix}$ is ______ (round off to nearest integer).

The product of the eigenvalues of the matrix $\begin{pmatrix} 2 &3 \\ 0& 7 \end{pmatrix}$ is ____________ (rounded off to one decimal place).

A set of simultaneous linear algebraic equations is represented in a matrix form as shown below.$\begin{bmatrix} 0 &0 &0 &4 &13 \\ 2& 5& 5& 2& 10\\ 0&0 &2 &5 &3 \\ 0&0 &0...

Which of the following statements are TRUE?P.The eigenvalues of a symmetric matrix are realQ.The value of the determinant of an orthogonal matrix can only be +1R.The tr...

Consider the following set of linear algebraic equations $x{_1} + 2x{_2} + 3x{_3} = 2$ ...