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## 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 $$\left[ {\matrix{ 0 &amp; 1 \cr { - 1} &amp; 0 \cr } } \right]$$
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 $$A = \left[ {\matrix{ 5 &amp; 3 \cr 1 &amp; 3 \cr } } \right],$$ ONE of the normalized eigen... GATE PI 2012 The eigen values of the following matrix $$\left[ {\matrix{ {10} &amp; { - 4} \cr {18} &amp; { - 12} \cr } ... GATE PI 2011 If$$(1, 0, -1){}^T$$is an eigen vector of the following matrix$$\left[ {\matrix{ 1 &amp; { - 1} &amp; 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 $$\left| {\matrix{ 1 &amp; 3 &amp; 2 \cr 4 &amp; 1 &amp; 1 \cr 2 &amp; 1 &amp;... GATE PI 2009 If$$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} &amp; b &amp; 1 \cr b &amp; {1 + b} &amp; 1 \cr 1 &amp; {2b} &am... GATE PI 2007 The eigen values of the matrix $$M$$ given are $$15, 3,$$ and $$0.$$ $$M = \left[ {\matrix{ 8 &amp; { - 6} &amp; 2 ... GATE PI 2005 Given matrix$$L = \left[ {\matrix{ 2 &amp; 1 \cr 3 &amp; 2 \cr 4 &amp; 5 \cr } } \right]\,\,$$and$$M... GATE PI 1994 For the following matrix $$\left[ {\matrix{ 1 &amp; { - 1} \cr 2 &amp; 3 \cr } } \right]$$ the number of pos... GATE PI 1994 The matrix $$\left[ {\matrix{ 1 &amp; { - 4} \cr 1 &amp; { - 5} \cr } } \right]$$ 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 $$\left[ {\matrix{ 1 &amp; 4 &amp; 9 \cr 4 &amp; 9 &amp; {16} \cr 9 ... GATE PI 1994 ## Marks 2 More$$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 &amp; 4 \cr 1 &amp; 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 $$\left[ {\matrix{ 0 &amp; 1 &amp; 0 \cr 1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 1 \cr... GATE PI 2008 The eigen vector pair of the matrix$$\left[ {\matrix{ 3 &amp; 4 \cr 4 &amp; { - 3} \cr } } \right]$\$ is
GATE PI 2008

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