GATE ME

Linear Algebra

Engineering Mathematics

(Past Years Questions)

Marks 1

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The determinant of a $$2 \times 2$$ matrix is $$50.$$ If one eigenvalue of the matrix is $$10,$$ the other eigenvalue is...
GATE ME 2017 Set 2
The product of eigenvalues of the matrix $$P$$ is $$P = \left[ {\matrix{ 2 & 0 & 1 \cr 4 & { - 3} & 3 \cr 0...
GATE ME 2017 Set 1
A real square matrix $$A$$ is called skew-symmetric if
GATE ME 2016 Set 3
The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & k \cr } } \right]...
GATE ME 2016 Set 2
The solution to the system of equations is $$\left[ {\matrix{ 2 & 5 \cr { - 4} & 3 \cr } } \right]\left\{ {\...
GATE ME 2016 Set 1
The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{ 4 & 2 \cr 1 & 3 \cr } } \right]$$ is ...
GATE ME 2015 Set 3
At least one eigenvalue of a singular matrix is
GATE ME 2015 Set 2
If any two columns of a determinant $$P = \left| {\matrix{ 4 & 7 & 8 \cr 3 & 1 & 5 \cr 9 & 6 & 2 \cr } ...
GATE ME 2015 Set 1
Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$...
GATE ME 2014 Set 4
Consider a $$3 \times 3$$ real symmetric matrix $$S$$ such that two of its eigen values are $$a \ne 0,$$ $$b\,\, \ne 0$$...
GATE ME 2014 Set 3
Given that the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 0 \cr 2 & 6 & 4 \cr { - 1} & 0 & 2 \cr...
GATE ME 2014 Set 1
Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\...
GATE ME 2014 Set 1
The eigen values of a symmetric matrix are all
GATE ME 2013
For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors...
GATE ME 2012
Eigen values of a real symmetric matrix are always
GATE ME 2011
Consider the following system of equations $$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0...
GATE ME 2011
One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 & 2 \cr 1 & 3 \cr } } \right]$$ is
GATE ME 2010
For a matrix $$\left[ M \right] = \left[ {\matrix{ {{3 \over 5}} & {{4 \over 5}} \cr x & {{3 \over 5}} \cr }...
GATE ME 2009
The matrix $$\left[ {\matrix{ 1 & 2 & 4 \cr 3 & 0 & 6 \cr 1 & 1 & P \cr } } \right]$$ has one eigen val...
GATE ME 2008
For what values of 'a' if any will the following system of equations in $$x, y$$ and $$z$$ have a solution? $$$2x+3y=4,$...
GATE ME 2008
If a square matrix $$A$$ is real and symmetric then the eigen values
GATE ME 2007
The number of linearly independent eigen vectors of $$\left[ {\matrix{ 2 & 1 \cr 0 & 2 \cr } } \right]$$ is
GATE ME 2007
$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$...
GATE ME 2005
For what value of $$x$$ will the matrix given below become singular? $$\left[ {\matrix{ 8 & x & 0 \cr 4 & 0 & 2 ...
GATE ME 2004
The sum of the eigen values of the matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr ...
GATE ME 2004
For the following set of simultaneous equations $$$1.5x - 0.5y + z = 2$$$ $$$4x + 2y + 3z = 9$$$ $$$7x + y + 5z = 10$$$
GATE ME 1997
The eigen values of $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & 1 & 1 \cr 1 & 1 & 1 \cr } } \right]$$ are
GATE ME 1996
In the Gauss - elimination for a solving system of linear algebraic equations, triangularization leads to
GATE ME 1996
Solve the system $$2x+3y+z=9,$$ $$4x+y=7,$$ $$x-3y-7z=6$$
GATE ME 1995
Among the following, the pair of vectors orthogonal to each other is
GATE ME 1995
Find out the eigen value of the matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 2 & 3 & 1 \cr 0 & 2 & 4 \cr ...
GATE ME 1994

Marks 2

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Consider the matrix $$A = \left[ {\matrix{ {50} & {70} \cr {70} & {80} \cr } } \right]$$ whose eigenvectors ...
GATE ME 2017 Set 2
The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{ 2 & 1 & 0 \cr 0 & 2 & 0 \cr ...
GATE ME 2016 Set 3
For a given matrix $$P = \left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right],$$ where $$i =...
GATE ME 2015 Set 3
Choose the CORRECT set of functions, which are linearly dependent.
GATE ME 2013
$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$ The system of algebraic equations given above has
GATE ME 2012
The eigen vectors of the matrix $$\left[ {\matrix{ 1 & 2 \cr 0 & 2 \cr } } \right]$$ are written in the form...
GATE ME 2008
Eigen values of a matrix $$S = \left[ {\matrix{ 3 & 2 \cr 2 & 3 \cr } } \right]$$ are $$5$$ and $$1.$$ What ...
GATE ME 2006
Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are $$E = \left[ {\matrix{ {\cos \thet...
GATE ME 2006
Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 & 0 & 0 & 0 \cr 0 & 5 & 0 & 0 ...
GATE ME 2005

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