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GATE PI

Linear Algebra

Engineering Mathematics

Previous Years Questions

Marks 1

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The number of solutions of the simultaneous algebraic equations $$y=3x+3$$ and $$y=3x+5$$ is
GATE PI 2016
The eigen values of the matrix are $$\left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right]$$
GATE PI 2016
The system of equations, given below, has $$$x+2y+4z=2$$$ $$$4x+3y+z=5$$$ $$$3x+2y+3z=1$$$
GATE PI 2014
For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen...
GATE PI 2012
The eigen values of the following matrix $$\left[ {\matrix{ {10} & { - 4} \cr {18} & { - 12} \cr } ...
GATE PI 2011
If $$(1, 0, -1)$$$${}^T$$ is an eigen vector of the following matrix $$\left[ {\matrix{ 1 & { - 1} & 0 \cr ...
GATE PI 2010
The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is...
GATE PI 2010
The value of the determinant $$\left| {\matrix{ 1 & 3 & 2 \cr 4 & 1 & 1 \cr 2 & 1 &...
GATE PI 2009
If $$A$$ is square symmetric real valued matrix of dimension $$2n$$, then the eigen values of $$A$$ are
GATE PI 2007
The determinant $$\left| {\matrix{ {1 + b} & b & 1 \cr b & {1 + b} & 1 \cr 1 & {2b} &am...
GATE PI 2007
The eigen values of the matrix $$M$$ given are $$15, 3, $$ and $$0.$$ $$M = \left[ {\matrix{ 8 & { - 6} & 2 ...
GATE PI 2005
Given matrix $$L = \left[ {\matrix{ 2 & 1 \cr 3 & 2 \cr 4 & 5 \cr } } \right]\,\,$$ and $$M...
GATE PI 1994
For the following matrix $$\left[ {\matrix{ 1 & { - 1} \cr 2 & 3 \cr } } \right]$$ the number of pos...
GATE PI 1994
The matrix $$\left[ {\matrix{ 1 & { - 4} \cr 1 & { - 5} \cr } } \right]$$ is an inverse of the matri...
GATE PI 1994
If for a matrix, rank equals both the number of rows and number of columns, then the matrix is called
GATE PI 1994
The value of the following determinant $$\left[ {\matrix{ 1 & 4 & 9 \cr 4 & 9 & {16} \cr 9 ...
GATE PI 1994

Marks 2

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$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$ The system of algebraic equations given above has
GATE PI 2012
If a matrix $$A = \left[ {\matrix{ 2 & 4 \cr 1 & 3 \cr } } \right]$$ and matrix $$B = \left[ {\matri...
GATE PI 2011
The value of $${x_3}$$ obtained by solving the following system of linear equations is $$${x_1} + 2{x_2} - 2{x_3} = 4$$...
GATE PI 2009
The inverse of matrix $$\left[ {\matrix{ 0 & 1 & 0 \cr 1 & 0 & 0 \cr 0 & 0 & 1 \cr...
GATE PI 2008
The eigen vector pair of the matrix $$\left[ {\matrix{ 3 & 4 \cr 4 & { - 3} \cr } } \right]$$ is
GATE PI 2008

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