## Marks 1

The determinant of a $$2 \times 2$$ matrix is $$50.$$ If one eigenvalue of the matrix is $$10,$$ the other eigenvalue is __________.

The product of eigenvalues of the matrix $$P$$ is $$P = \left[ {\matrix{
2 & 0 & 1 \cr
4 & { - 3} & 3 \cr
0 & 2 &...

A real square matrix $$A$$ is called skew-symmetric if

The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{
2 & 1 \cr
1 & k \cr
} } \right]$$ are positive, is

The solution to the system of equations is $$\left[ {\matrix{
2 & 5 \cr
{ - 4} & 3 \cr
} } \right]\left\{ {\matrix{
x \cr
...

The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{
4 & 2 \cr
1 & 3 \cr
} } \right]$$ is ______.

At least one eigenvalue of a singular matrix is

If any two columns of a determinant $$P = \left| {\matrix{
4 & 7 & 8 \cr
3 & 1 & 5 \cr
9 & 6 & 2 \cr
} } \rig...

Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$?

Consider a $$3 \times 3$$ real symmetric matrix $$S$$ such that two of its eigen values are $$a \ne 0,$$ $$b\,\, \ne 0$$ with respective eigen vectors...

Given that the determinant of the matrix $$\left[ {\matrix{
1 & 3 & 0 \cr
2 & 6 & 4 \cr
{ - 1} & 0 & 2 \cr
} ...

Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\,\,2\widehat i + 3\widehat j +...

The eigen values of a symmetric matrix are all

For the matrix $$A = \left[ {\matrix{
5 & 3 \cr
1 & 3 \cr
} } \right],$$ ONE of the normalized eigen vectors is given as

Eigen values of a real symmetric matrix are always

Consider the following system of equations
$$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0.$$
This system has

One of the eigen vector of the matrix $$A = \left[ {\matrix{
2 & 2 \cr
1 & 3 \cr
} } \right]$$ is

For a matrix $$\left[ M \right] = \left[ {\matrix{
{{3 \over 5}} & {{4 \over 5}} \cr
x & {{3 \over 5}} \cr
} } \right].$$ The tran...

The matrix $$\left[ {\matrix{
1 & 2 & 4 \cr
3 & 0 & 6 \cr
1 & 1 & P \cr
} } \right]$$ has one eigen value to ...

For what values of 'a' if any will the following system of equations in $$x, y$$ and $$z$$ have a solution?
$$$2x+3y=4,$$$
$$$x+y+z=4,$$$
$$$x+2y-z=a$...

If a square matrix $$A$$ is real and symmetric then the eigen values

The number of linearly independent eigen vectors of $$\left[ {\matrix{
2 & 1 \cr
0 & 2 \cr
} } \right]$$ is

$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$ is

For what value of $$x$$ will the matrix given below become singular? $$\left[ {\matrix{
8 & x & 0 \cr
4 & 0 & 2 \cr
{12} ...

The sum of the eigen values of the matrix $$\left[ {\matrix{
1 & 1 & 3 \cr
1 & 5 & 1 \cr
3 & 1 & 1 \cr
} } \r...

For the following set of simultaneous equations
$$$1.5x - 0.5y + z = 2$$$
$$$4x + 2y + 3z = 9$$$
$$$7x + y + 5z = 10$$$

In the Gauss - elimination for a solving system of linear algebraic equations, triangularization leads to

The eigen values of $$\left[ {\matrix{
1 & 1 & 1 \cr
1 & 1 & 1 \cr
1 & 1 & 1 \cr
} } \right]$$ are

Solve the system $$2x+3y+z=9,$$ $$4x+y=7,$$ $$x-3y-7z=6$$

Among the following, the pair of vectors orthogonal to each other is

Find out the eigen value of the matrix $$A = \left[ {\matrix{
1 & 0 & 0 \cr
2 & 3 & 1 \cr
0 & 2 & 4 \cr
} } \...

## Marks 2

Consider the matrix $$A = \left[ {\matrix{
{50} & {70} \cr
{70} & {80} \cr
} } \right]$$ whose eigenvectors corresponding to eigen...

The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{
2 & 1 & 0 \cr
0 & 2 & 0 \cr
0 & 0 &...

For a given matrix $$P = \left[ {\matrix{
{4 + 3i} & { - i} \cr
i & {4 - 3i} \cr
} } \right],$$ where $$i = \sqrt { - 1} ,$$ the...

Choose the CORRECT set of functions, which are linearly dependent.

$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$
The system of algebraic equations given above has

The eigen vectors of the matrix $$\left[ {\matrix{
1 & 2 \cr
0 & 2 \cr
} } \right]$$ are written in the form $$\left[ {\matrix{
...

Eigen values of a matrix $$S = \left[ {\matrix{
3 & 2 \cr
2 & 3 \cr
} } \right]$$ are $$5$$ and $$1.$$ What are the eigen values o...

Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are
$$E = \left[ {\matrix{
{\cos \theta } & { - sin\theta } &...

Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{
5 & 0 & 0 & 0 \cr
0 & 5 & 0 & 0 \cr
...