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## 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 $$P = \left[ {\matrix{ 2 &amp; 0 &amp; 1 \cr 4 &amp; { - 3} &a... GATE ME 2017 Set 1 A real square matrix$$A$$is called skew-symmetric if GATE ME 2016 Set 3 The condition for which the eigenvalues of the matrix$$A = \left[ {\matrix{ 2 &amp; 1 \cr 1 &amp; k \cr } }...
GATE ME 2016 Set 2
The solution to the system of equations is $$\left[ {\matrix{ 2 &amp; 5 \cr { - 4} &amp; 3 \cr } } \right]\l... GATE ME 2016 Set 1 The lowest eigen value of the$$2 \times 2$$matrix$$\left[ {\matrix{ 4 &amp; 2 \cr 1 &amp; 3 \cr } } \righ...
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 $$P = \left| {\matrix{ 4 &amp; 7 &amp; 8 \cr 3 &amp; 1 &amp; 5 \cr 9 &a... GATE ME 2015 Set 1 Which one of the following equations is a correct identity for arbitrary$$3 \times 3$$real matrices$$P,Q$$and$$R$$... GATE ME 2014 Set 4 Which one of the following describes the relationship among the three vectors,$$\widehat i + \widehat j + \widehat k,\...
GATE ME 2014 Set 1
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 $$\left[ {\matrix{ 1 &amp; 3 &amp; 0 \cr 2 &amp; 6 &amp; 4 \cr { -... GATE ME 2014 Set 1 The eigen values of a symmetric matrix are all GATE ME 2013 For the matrix$$A = \left[ {\matrix{ 5 &amp; 3 \cr 1 &amp; 3 \cr } } \right],$$ONE of the normalized eigen... GATE ME 2012 Consider the following system of equations$$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$and$${x_1} + {x_2} = 0...
GATE ME 2011
Eigen values of a real symmetric matrix are always
GATE ME 2011
One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 &amp; 2 \cr 1 &amp; 3 \cr } } \right]$$ is
GATE ME 2010
For a matrix $$\left[ M \right] = \left[ {\matrix{ {{3 \over 5}} &amp; {{4 \over 5}} \cr x &amp; {{3 \over 5}} ... GATE ME 2009 For what values of 'a' if any will the following system of equations in$$x, y$$and$$z$$have a solution?$$$2x+3y=4,$...
GATE ME 2008
The matrix $$\left[ {\matrix{ 1 &amp; 2 &amp; 4 \cr 3 &amp; 0 &amp; 6 \cr 1 &amp; 1 &amp; P \cr } } \ri... GATE ME 2008 The number of linearly independent eigen vectors of$$\left[ {\matrix{ 2 &amp; 1 \cr 0 &amp; 2 \cr } } \righ...
GATE ME 2007
If a square matrix $$A$$ is real and symmetric then the eigen values
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
The sum of the eigen values of the matrix $$\left[ {\matrix{ 1 &amp; 1 &amp; 3 \cr 1 &amp; 5 &amp; 1 \cr 3 ... GATE ME 2004 For what value of$$x$$will the matrix given below become singular?$$\left[ {\matrix{ 8 &amp; x &amp; 0 \cr 4 ...
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
In the Gauss - elimination for a solving system of linear algebraic equations, triangularization leads to
GATE ME 1996
The eigen values of $$\left[ {\matrix{ 1 &amp; 1 &amp; 1 \cr 1 &amp; 1 &amp; 1 \cr 1 &amp; 1 &amp; 1 \cr ... GATE ME 1996 Among the following, the pair of vectors orthogonal to each other is GATE ME 1995 Solve the system$$2x+3y+z=9,4x+y=7,x-3y-7z=6$$GATE ME 1995 Find out the eigen value of the matrix$$A = \left[ {\matrix{ 1 &amp; 0 &amp; 0 \cr 2 &amp; 3 &amp; 1 \cr 0...
GATE ME 1994

## Marks 2

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

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