## Marks 1

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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 $$A = \left[ {\matrix{ k & {2k} \cr {{k^2} - k} & {{k^2}} \cr } } \right]$$ and vector $$X =... GATE ECE 2018 The rank of the matrix$$M = \left[ {\matrix{ 5 & {10} & {10} \cr 1 & 0 & 2 \cr 3 & 6 & 6 \cr } } \righ...
GATE ECE 2017 Set 1
Consider the $$5 \times 5$$ matrix $$A = \left[ {\matrix{ 1 & 2 & 3 & 4 & 5 \cr 5 & 1 & 2 & 3 & 4 \cr 4 & 5... GATE ECE 2017 Set 1 Consider a$$2 \times 2$$square matrix$$A = \left[ {\matrix{ \sigma & x \cr \omega & \sigma \cr } } \ri...
GATE ECE 2016 Set 3
The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 9 & 7 & {13} \cr { - 6} & { - ... GATE ECE 2016 Set 2 Let$${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 & {\tan x} \cr { - \tan x} & 1 \cr } } \right],$$the determinant of$${A^T}\,{...
GATE ECE 2015 Set 3
The value of $$'x'$$ for which all the eigenvalues of the matrix given below are real is $$\left[ {\matrix{ {10} & {... GATE ECE 2015 Set 2 Consider system of linear equations :$$$x-2y+3z=-1$x-3y+4z=1$$and$$$-2x+4y-6z=k,$$The value of$$'k'$$for... GATE ECE 2015 Set 1 The value of$$'P'$$such that the vector$$\left[ {\matrix{ 1 \cr 2 \cr 3 \cr } } \right]$$is an eig... GATE ECE 2015 Set 1 Which one of the following statements is NOT true for a square matrix$$A$$? GATE ECE 2014 Set 3 The determinant of matrix$$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 $$\left( {\matrix{ 2 & 1 & 3 \cr 3 & 0 & 1 \cr 1 & 2 & 5 \cr } } \right)... GATE ECE 2014 Set 2 The maximum value of the determinant among all$$2 \times 2$$real symmetric matrices with trace$$14$$is ______. GATE ECE 2014 Set 2 For matrices of same dimension$$M,N$$and scalar$$c,$$which one of these properties DOES NOT ALWAYS hold ? GATE ECE 2014 Set 1$$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 $${J_6} = \left[ {\matrix{ 0 & 0 & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 & 0 & 1 & 0 \cr 0 & 0 & ... GATE ECE 2014 Set 1 The minimum eigenvalue of the following matrix is$$\left[ {\matrix{ 3 & 5 & 2 \cr 5 & {12} & 7 \cr 2 & 7 &...
GATE ECE 2013
Let $$A$$ be an $$m\,\, \times \,\,n$$ matrix and $$B$$ an $$n\,\, \times \,\,m$$ matrix. It is given that determinant $... GATE ECE 2013 Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matri... GATE ECE 2012 The system of equations$$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 All the four entries of $$2$$ $$x$$ $$2$$ matrix $$P = \left[ {\matrix{ {{p_{11}}} & {{p_{12}}} \cr {{p_{21}}} ... GATE ECE 2008 The system of linear equations$$\left. {\matrix{ {4x + 2y = 7} \cr {2x + y = 6} \cr } } \right\}$$has GATE ECE 2008 For the matrix$$\left[ {\matrix{ 4 & 2 \cr 2 & 4 \cr } } \right].$$The eigen value corresponding to the ei... GATE ECE 2006 The rank of the matrix$$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr } } \right]$$... GATE ECE 2006 The eigen values of the matrix$$\left[ {\matrix{ 2 & { - 1} & 0 & 0 \cr 0 & 3 & 0 & 0 \cr 0 & 0 & { - 2} &... GATE ECE 2000 The eigen values of the matrix $$A = \left[ {\matrix{ 0 & 1 \cr 1 & 0 \cr } } \right]$$ are GATE ECE 1998 The rank of $$\left( {m \times n} \right)$$ matrix $$\left( {m GATE ECE 1994 The following system of equations$${{x_1} + {x_2} + {x_3} = 3}{{x_1} - {x_3} = 0}{{x_1} - {x_2} + {x_3} = 1}... GATE ECE 1994 ## Marks 2 More The rank of the matrix $$\left[ {\matrix{ 1 & { - 1} & 0 & 0 & 0 \cr 0 & 0 & 1 & { - 1} & 0 \cr 0 & 1 & { -... GATE ECE 2017 Set 2 If the vectors$${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 $$A = \left[ {\matrix{ a & 0 & 3 & 7 \cr 2 & 5 & 1 & 3 \cr 0 & 0 & 2 & 4 \cr 0 & 0 & 0 & b ... GATE ECE 2016 Set 2 A sequence$$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 $$\left[ {\matrix{ { - 1} & 3 & 5 \cr { - 3} & { - 1} & 6 \cr 0 & ... GATE ECE 2009 The eigen values and the correspondinng eigen vectors of a$$2 \times 2$$matrix are given by Eigen value$${\lambda _1...
GATE ECE 2006
Given an orthogonal matrix $$A = \left[ {\matrix{ 1 & 1 & 1 & 1 \cr 1 & 1 & { - 1} & { - 1} \cr 1 & { - 1} ... GATE ECE 2005 Given the matrix$$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$the eigen vector is GATE ECE 2005 If$$A = \left[ {\matrix{ 2 & { - 0.1} \cr 0 & 3 \cr } } \right]$$and$${A^{ - 1}} = \left[ {\matrix{ {{...
GATE ECE 2005

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