List of top Mathematics Questions on Linear Algebra asked in TS PGECET

The eigenvalues of a $3\times3$ real matrix $A$ are $0$, $-2$, $-2$ and it satisfies the equation \[ A^4+4A^3=KA^2, \] then the value of $K$ is

If $P$ is an orthogonal matrix of order $3\times3$, $A=\begin{bmatrix}1& 2& 2\\2& 1& 2\\2& 2& 1\end{bmatrix}$ and the eigenvalues of $P^{T}AP$ are $\alpha,\beta,\gamma$, then $\alpha^2+\beta^2+\gamma^2=$

The eigenvalues of a $3\times3$ real matrix $A$ are $0$, $-2$, $-2$ and it satisfies the equation \[ A^4+4A^3=KA^2, \] then the value of $K$ is

An eigen vector of the matrix \[ A= \begin{bmatrix} 3 & 2 1 & 2 \end{bmatrix} \] is

If $P$ is an orthogonal matrix of order $3\times3$, $A=\begin{bmatrix}1& 2& 2\\2& 1& 2\\2& 2& 1\end{bmatrix}$ and the eigenvalues of $P^{T}AP$ are $\alpha,\beta,\gamma$, then $\alpha^2+\beta^2+\gamma^2=$

If \[ \{(2,-3,5),\ (1,\alpha,7),\ (3,\beta,3)\} \] is not a basis of the vector space $\mathbb{R}^3$, then $(\alpha,\beta)$ lies on the locus:

An Eigen value of the matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ is $1$. An eigen vector corresponding to it is:}

Consider the linear system of equations \[ \begin{bmatrix} 3 & -1 & 4 \\ 6 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \end{bmatrix}. \] In this system of equations, if $x$ is always a fixed constant, then the system has:& nbsp;