Questions without a selected answer in Linear Algebra

Which of the following is one of the eigenvalues for the matrix given below?\[\left[\begin{array}{cc}3 & 4 \\4 & -3\end{array}\right]\]$1$$3$$5$$7$

For the given matrix, which of the statements given below is/are true?\[\left[\begin{array}{ccc}3 & 1 & 5 \\2 & -1 & 0 \\5 & 2 & 9\end{array}\right]\]The matrix is full r...

If the straight lines given by the following two equations are parallel to each other, the value of $\boldsymbol{a}$ is $\_\_\_\_$. (answer in integer)\[4 x+7 y=6 ; \quad...

The value of $k$, for which the linear equations $2 x+3 y=6$ and $4 x+6 y=3 k$ have at least one solution, is $\_\_\_\_\_$ (Answer in integer)

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 $\_\_\_\_...

A value of $k$ for which the linear equations $(k-1) x+3 y=0$ and $2 x+k y=0$ have a non-zero solution is $\_\_\_\_\_\_\_$.$1$$2$$3$$4$

If $A=\left(\begin{array}{ll}1 & 2 \\ 3 & 5\end{array}\right)$, the value of $\left|A^{4}+3 A^{2}-5 A+6 I\right|$ 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...

The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.

The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.

The system of linear equations$$cx+y=5$$$$3x+3y=6$$has no solution when $c$ is equal to _______________________.

Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.

The positive Eigen value of the following matrix is __________. $$\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$$

The value of determinant $A$ given below is ________.$A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$

The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $$\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{b...

The determinant of the matrix $\begin{bmatrix} 3 & 0 & 0 \\ 2 & 5 & 0 \\ 6 & -8 & -4 \end{bmatrix}$ is __________

$$\begin{array}{cc} 2x_1+ x_2 = 35 \\ 5x_1 + bx_2 = 7.5 \end{array}$$ The system of linear equations in two variables shown above will have infinite solutions, if and onl...

What are the eigenvalues of the following matrix? $$\begin{bmatrix} 1 & 1 \\ -2 & 4 \end{bmatrix}$$$2$ and $3$$-2$ and $3$$2$ and $-3$$-2$ and $-3$

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...

The eigenvalues of A =$\begin{bmatrix} 1&-4\\2 & -3 \end{bmatrix} $are$2\underline{+}i$$-1, -2$$-1\underline{+}2i$non-existent

The solution for the following set of equations is,$$5x+4y+102=13$$$$x+3y+z=7$$$$4x2y+z=0$$$x=2,y=1,z=1$$x=1,y=2,z=0$$x=1,y=0,z=2$$x=0,y=1,z=2$

The solution to the following set of equations is$$2x+3y=4$$$$4x+6y=0$$$x=0,y=0$$x=2, y=0$$4x=-6y$No solution

The solution of the following set of equations is$$x+2y+3z=20$$$$7x+3y+z=13$$$$x+6y+2z=0$$$x=-2, y=2, z=8$$x=2, y=-3, z=8$$x=2, y=3, z=-8$$x=8, y=2, z=-3$

One of the eigcn values of $P=\begin{bmatrix}10 & -4 \\ 18 & -12\end{bmatrix}$ is$2$$4$$6$$8$

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...

What is the rank of the following matrix?$$\begin{bmatrix}5 & 3 & -1\\ 6 & 2 & -4 \\14 & 10 & 0 \end{bmatrix}$$$0$$1$$2$$3$