Linear Algebra · Engineering Mathematics · GATE ME

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Marks 1

GATE ME 2017 Set 2
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 1
The product of eigenvalues of the matrix $$P$$ is $$P = \left[ {\matrix{ 2 & 0 & 1 \cr 4 & { - 3} & 3 \cr 0 & 2 &...
GATE ME 2016 Set 3
A real square matrix $$A$$ is called skew-symmetric if
GATE ME 2016 Set 2
The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & k \cr } } \right]$$ are positive, is
GATE ME 2016 Set 1
The solution to the system of equations is $$\left[ {\matrix{ 2 & 5 \cr { - 4} & 3 \cr } } \right]\left\{ {\matrix{ x \cr ...
GATE ME 2015 Set 3
The lowest eigen value of the $$2 \times 2$$ matrix $$\left[ {\matrix{ 4 & 2 \cr 1 & 3 \cr } } \right]$$ is ______.
GATE ME 2015 Set 2
At least one eigenvalue of a singular matrix is
GATE ME 2015 Set 1
If any two columns of a determinant $$P = \left| {\matrix{ 4 & 7 & 8 \cr 3 & 1 & 5 \cr 9 & 6 & 2 \cr } } \rig...
GATE ME 2014 Set 4
Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$?
GATE ME 2014 Set 3
Consider a $$3 \times 3$$ real symmetric matrix $$S$$ such that two of its eigen values are $$a \ne 0,$$ $$b\,\, \ne 0$$ with respective eigen vectors...
GATE ME 2014 Set 1
Given that the determinant of the matrix $$\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, $$\widehat i + \widehat j + \widehat k,\,\,2\widehat i + 3\widehat j +...
GATE ME 2013
The eigen values of a symmetric matrix are all
GATE ME 2012
For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as
GATE ME 2011
Eigen values of a real symmetric matrix are always
GATE ME 2011
Consider the following system of equations $$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0.$$ This system has
GATE ME 2010
One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 & 2 \cr 1 & 3 \cr } } \right]$$ is
GATE ME 2009
For a matrix $$\left[ M \right] = \left[ {\matrix{ {{3 \over 5}} & {{4 \over 5}} \cr x & {{3 \over 5}} \cr } } \right].$$ The tran...
GATE ME 2008
The matrix $$\left[ {\matrix{ 1 & 2 & 4 \cr 3 & 0 & 6 \cr 1 & 1 & P \cr } } \right]$$ has one eigen value to ...
GATE ME 2008
For what values of 'a' if any will the following system of equations in $$x, y$$ and $$z$$ have a solution? $$$2x+3y=4,$$$ $$$x+y+z=4,$$$ $$$x+2y-z=a$...
GATE ME 2007
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 2005
$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$ is
GATE ME 2004
For what value of $$x$$ will the matrix given below become singular? $$\left[ {\matrix{ 8 & x & 0 \cr 4 & 0 & 2 \cr {12} ...
GATE ME 2004
The sum of the eigen values of the matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr } } \r...
GATE ME 1997
For the following set of simultaneous equations $$$1.5x - 0.5y + z = 2$$$ $$$4x + 2y + 3z = 9$$$ $$$7x + y + 5z = 10$$$
GATE ME 1996
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 1995
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 1994
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

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