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## Marks 1

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Let $$\alpha$$, $$\beta$$ two non-zero real numbers and v1, v2 be two non-zero real vectors of size 3 $$\times$$ 1. Supp...
GATE ECE 2022
Consider a system of linear equations Ax = b, where $$A = \left[ {\matrix{ 1 \hfill & { - \sqrt 2 } \hfill & 3 \hfill... GATE ECE 2022 Let M be a real 4$$ \times $$4 matrix. Consider the following statements : S1: M has 4 linearly independent eigenvecto... GATE ECE 2018 Consider matrix$$A = \left[ {\matrix{ k &amp; {2k} \cr {{k^2} - k} &amp; {{k^2}} \cr } } \right]$$and vect... GATE ECE 2018 Consider the$$5 \times 5$$matrix$$A = \left[ {\matrix{ 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 \cr 5 &amp; 1 &amp; ...
GATE ECE 2017 Set 1
The rank of the matrix $$M = \left[ {\matrix{ 5 &amp; {10} &amp; {10} \cr 1 &amp; 0 &amp; 2 \cr 3 &amp; 6 &... GATE ECE 2017 Set 1 Consider a$$2 \times 2$$square matrix$$A = \left[ {\matrix{ \sigma &amp; x \cr \omega &amp; \sigma \cr ...
GATE ECE 2016 Set 3
The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 &amp; 2 &amp; 4 \cr 9 &amp; 7 &amp; {13} \cr ... GATE ECE 2016 Set 2 Let$${M^4} = {\rm I}$$(where$${\rm I}$$denotes the identity matrix) and$$M \ne {\rm I},\,\,{M^2} \ne {\rm I}$$and ... GATE ECE 2016 Set 1 For$$A = \left[ {\matrix{ 1 &amp; {\tan x} \cr { - \tan x} &amp; 1 \cr } } \right],$$the determinant of$$...
GATE ECE 2015 Set 3
The value of $$'x'$$ for which all the eigenvalues of the matrix given below are real is $$\left[ {\matrix{ {10} &am... GATE ECE 2015 Set 2 The value of$$'P'$$such that the vector$$\left[ {\matrix{ 1 \cr 2 \cr 3 \cr } } \right]$$is an eig... GATE ECE 2015 Set 1 Consider system of linear equations :$$$x-2y+3z=-1$x-3y+4z=1$$and$$$-2x+4y-6z=k,$$The value of$$'k'$$for... GATE ECE 2015 Set 1 The maximum value of the determinant among all$$2 \times 2$$real symmetric matrices with trace$$14$$is ______. GATE ECE 2014 Set 2 Which one of the following statements is NOT true for a square matrix$$A$$? GATE ECE 2014 Set 3$$A$$real$$\left( {4\,\, \times \,\,4} \right)$$matrix$$A$$satisfies the equation$${A^2} = {\rm I},$$where$${\rm... GATE ECE 2014 Set 1 Consider the matrix $${J_6} = \left[ {\matrix{ 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 \cr 0 &amp; 0 &amp; 0 &... GATE ECE 2014 Set 1 The determinant of matrix$$A$$is$$5$$and the determinant of matrix$$B$$is$$40.$$The determinant of matrix$$AB$...
GATE ECE 2014 Set 2
The system of linear equations $$\left( {\matrix{ 2 &amp; 1 &amp; 3 \cr 3 &amp; 0 &amp; 1 \cr 1 &amp; 2 &am... GATE ECE 2014 Set 2 For matrices of same dimension$$M,N$$and scalar$$c,$$which one of these properties DOES NOT ALWAYS hold ? GATE ECE 2014 Set 1 Let$$A$$be an$$m\,\, \times \,\,n$$matrix and$$B$$an$$n\,\, \times \,\,m$$matrix. It is given that determinant ... GATE ECE 2013 The minimum eigenvalue of the following matrix is$$\left[ {\matrix{ 3 &amp; 5 &amp; 2 \cr 5 &amp; {12} &amp; 7 ...
GATE ECE 2013
Given that $$A = \left[ {\matrix{ { - 5} &amp; { - 3} \cr 2 &amp; 0 \cr } } \right]$$ and $${\rm I} = \left[... GATE ECE 2012 The system of equations$$x+y+z=6,x+4y+6z=20,x + 4y + \lambda z = \mu $$has no solution for values of$$\lamb...
GATE ECE 2011
The eigen values of a skew-symmetric matrix are
GATE ECE 2010
The system of linear equations $$\left. {\matrix{ {4x + 2y = 7} \cr {2x + y = 6} \cr } } \right\}$$ has
GATE ECE 2008
All the four entries of $$2$$ $$x$$ $$2$$ matrix $$P = \left[ {\matrix{ {{p_{11}}} &amp; {{p_{12}}} \cr {{p_{21... GATE ECE 2008 The rank of the matrix$$\left[ {\matrix{ 1 &amp; 1 &amp; 1 \cr 1 &amp; { - 1} &amp; 0 \cr 1 &amp; 1 &amp; ...
GATE ECE 2006
For the matrix $$\left[ {\matrix{ 4 &amp; 2 \cr 2 &amp; 4 \cr } } \right].$$ The eigen value corresponding t...
GATE ECE 2006
The eigen values of the matrix $$\left[ {\matrix{ 2 &amp; { - 1} &amp; 0 &amp; 0 \cr 0 &amp; 3 &amp; 0 &amp; 0 ... GATE ECE 2000 The eigen values of the matrix$$A = \left[ {\matrix{ 0 &amp; 1 \cr 1 &amp; 0 \cr } } \right]$$are GATE ECE 1998 The rank of$$\left( {m \times n} \right)$$matrix$$\left( {m &lt; n} \right)$$cannot be more then GATE ECE 1994 The following system of equations$${{x_1} + {x_2} + {x_3} = 3}{{x_1} - {x_3} = 0}{{x_1} - {x_2} + {x_3} = 1}...
GATE ECE 1994

## Marks 2

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The rank of the matrix $$\left[ {\matrix{ 1 &amp; { - 1} &amp; 0 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 1 &amp; { -... GATE ECE 2017 Set 2 If the vectors$${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$and$${e_3} = \left( { - 2,0,1} \righ...
GATE ECE 2016 Set 3
The matrix $$A = \left[ {\matrix{ a &amp; 0 &amp; 3 &amp; 7 \cr 2 &amp; 5 &amp; 1 &amp; 3 \cr 0 &amp; 0 &am... GATE ECE 2016 Set 2 A sequence$$x\left[ n \right]$$is specified as$$\$\left[ {\matrix{ {x\left[ n \right]} \cr {x\left[ {n - 1} \...
GATE ECE 2016 Set 1
The eigen values of the following matrix $$\left[ {\matrix{ { - 1} &amp; 3 &amp; 5 \cr { - 3} &amp; { - 1} &amp;... GATE ECE 2009 The eigen values and the correspondinng eigen vectors of a$$2 \times 2$$matrix are given by Eigen value$${\lambda _1...
GATE ECE 2006
If $$A = \left[ {\matrix{ 2 &amp; { - 0.1} \cr 0 &amp; 3 \cr } } \right]$$ and $${A^{ - 1}} = \left[ {\matri... GATE ECE 2005 Given the matrix$$\left[ {\matrix{ { - 4} &amp; 2 \cr 4 &amp; 3 \cr } } \right],$$the eigen vector is GATE ECE 2005 Given an orthogonal matrix$$A = \left[ {\matrix{ 1 &amp; 1 &amp; 1 &amp; 1 \cr 1 &amp; 1 &amp; { - 1} &amp; { -...
GATE ECE 2005

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