# 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
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