Marks 1
The eigen values of the matrix are $$\left[ {\matrix{
0 & 1 \cr
{ - 1} & 0 \cr
} } \right]$$
The number of solutions of the simultaneous algebraic equations $$y=3x+3$$ and $$y=3x+5$$ is
The system of equations, given below, has
$$$x+2y+4z=2$$$
$$$4x+3y+z=5$$$
$$$3x+2y+3z=1$$$
For the matrix $$A = \left[ {\matrix{
5 & 3 \cr
1 & 3 \cr
} } \right],$$ ONE of the normalized eigen vectors is given as
The eigen values of the following matrix $$\left[ {\matrix{
{10} & { - 4} \cr
{18} & { - 12} \cr
} } \right]$$ are
The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is
If $$(1, 0, -1)$$$${}^T$$ is an eigen vector of the following matrix $$\left[ {\matrix{
1 & { - 1} & 0 \cr
{ - 1} & 2 & { - 1}...
The value of the determinant $$\left| {\matrix{
1 & 3 & 2 \cr
4 & 1 & 1 \cr
2 & 1 & 3 \cr
} } \right|$$ is
If $$A$$ is square symmetric real valued matrix of dimension $$2n$$, then the eigen values of $$A$$ are
The determinant $$\left| {\matrix{
{1 + b} & b & 1 \cr
b & {1 + b} & 1 \cr
1 & {2b} & 1 \cr
} } \right|$$ equ...
The eigen values of the matrix $$M$$ given are $$15, 3, $$ and $$0.$$
$$M = \left[ {\matrix{
8 & { - 6} & 2 \cr
{ - 6} & 7 & ...
If for a matrix, rank equals both the number of rows and number of columns, then the matrix is called
The value of the following determinant $$\left[ {\matrix{
1 & 4 & 9 \cr
4 & 9 & {16} \cr
9 & {16} & {25} \cr
...
The matrix $$\left[ {\matrix{
1 & { - 4} \cr
1 & { - 5} \cr
} } \right]$$ is an inverse of the matrix $$\left[ {\matrix{
5 &...
For the following matrix $$\left[ {\matrix{
1 & { - 1} \cr
2 & 3 \cr
} } \right]$$ the number of positive characteristic roots is
Given matrix $$L = \left[ {\matrix{
2 & 1 \cr
3 & 2 \cr
4 & 5 \cr
} } \right]\,\,$$ and $$M = \left[ {\matrix{
3 &...
Marks 2
$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$
The system of algebraic equations given above has
If a matrix $$A = \left[ {\matrix{
2 & 4 \cr
1 & 3 \cr
} } \right]$$ and matrix $$B = \left[ {\matrix{
4 & 6 \cr
5 &am...
The value of $${x_3}$$ obtained by solving the following system of linear equations is
$$${x_1} + 2{x_2} - 2{x_3} = 4$$$
$$$2{x_1} + {x_2} + {x_3} = ...
The eigen vector pair of the matrix $$\left[ {\matrix{
3 & 4 \cr
4 & { - 3} \cr
} } \right]$$ is
The inverse of matrix $$\left[ {\matrix{
0 & 1 & 0 \cr
1 & 0 & 0 \cr
0 & 0 & 1 \cr
} } \right]$$ is