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The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the followin...
GATE CE 2017 Set 1
Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$3{x_1} + 2{x_2} = {c_1... GATE CE 2017 Set 2 If the entries in each column of a square matrix$$M$$add up to$$1$$, then an eigenvalue of$$M$$is GATE CE 2016 Set 1 Let$$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$with$$n \ge 3$$and$${{a_{ij}} = i.j.}$$The rank of$$A$$i... GATE CE 2015 Set 2 For what value of$$'p'$$the following set of equations will have no solutions?$$$2x+3y=5$3x+py=10$$GATE CE 2015 Set 1 The rank of the matrix$$\left[ {\matrix{ 6 &amp; 0 &amp; 4 &amp; 4 \cr { - 2} &amp; {14} &amp; 8 &amp; {18} \c...
GATE CE 2014 Set 2
The determinant of matrix $$\left[ {\matrix{ 0 &amp; 1 &amp; 2 &amp; 3 \cr 1 &amp; 0 &amp; 3 &amp; 0 \cr 2 ... GATE CE 2014 Set 2 The sum of Eigen values of the matrix,$$\left[ M \right]$$is where$$\left[ M \right] = \left[ {\matrix{ {215} &am...
GATE CE 2014 Set 1
Given the matrices $$J = \left[ {\matrix{ 3 &amp; 2 &amp; 1 \cr 2 &amp; 4 &amp; 2 \cr 1 &amp; 2 &amp; 6 \c... GATE CE 2014 Set 1 The eigen values of matrix$$\left[ {\matrix{ 9 &amp; 5 \cr 5 &amp; 8 \cr } } \right]$$are GATE CE 2012 In the solution of the following set of linear equations by Gauss-elimination using partial pivoting$$$5x+y+2z=34,$$... GATE CE 2009 A square matrix$$B$$is symmetric if ____ GATE CE 2009 The following system of equations$$$x+y+z=3,$x+2y+3z=4,$x+4y+kz=6$$will not have a unique solution for ... GATE CE 2008 The eigenvalues of the matrix$$\left[ P \right] = \left[ {\matrix{ 4 &amp; 5 \cr 2 &amp; { - 5} \cr } } \ri...
GATE CE 2008
The product of matrices $${\left( {PQ} \right)^{ - 1}}P$$ is
GATE CE 2008
Solution for the system defined by the set of equations $$4y+3z=8, 2x-z=2$$ &amp; $$3x+2y=5$$ is
GATE CE 2006
Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda$$ is a scalar. L...
GATE CE 2005
Consider the matrices $$\,{X_{4x3,}}\,\,{Y_{4x3}}$$ $$\,\,{P_{2x3}}.$$ The order of $$\,{\left[ {P{{\left( {{X^T}Y} \ri... GATE CE 2005 Consider a non-homogeneous system of linear equations represents mathematically an over determined system. Such a system... GATE CE 2005 Consider the following system of equations in three real variable$${x_1},{x_2}$$and$${x_3}:$2{x_1} - {x_2} ... GATE CE 2005 The eigen values of the matrix $$\left[ {\matrix{ 4 &amp; { - 2} \cr { - 2} &amp; 1 \cr } } \right]$$ are GATE CE 2004 Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\... GATE CE 2004 Given matrix$$\left[ A \right] = \left[ {\matrix{ 4 &amp; 2 &amp; 1 &amp; 3 \cr 6 &amp; 3 &amp; 4 &amp; 7 \cr ... GATE CE 2003 Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} &amp; 4 \cr 4 &amp; { - 1} \cr } } \right... GATE CE 2002 The determinant of the following matrix$$\left[ {\matrix{ 5 &amp; 3 &amp; 2 \cr 1 &amp; 2 &amp; 6 \cr 3 &a... GATE CE 2001 The product $$\left[ P \right]\,\,{\left[ Q \right]^T}$$ of the following two matrices $$\left[ P \right]\,$$ and $$\lef... GATE CE 2001 The eigen values of the matrix$$\left[ {\matrix{ 5 &amp; 3 \cr 2 &amp; 9 \cr } } \right]$$are GATE CE 2001 If$$A,B,C$$are square matrices of the same order then$${\left( {ABC} \right)^{ - 1}}$$is equal be GATE CE 2000 Consider the following two statements.$$(I)$$The maximum number of linearly independent column vectors of a matrix$$... GATE CE 2000 The number of terms in the expansion of general determinant of order $$n$$ is GATE CE 1999 The equation $$\left[ {\matrix{ 2 &amp; 1 &amp; 1 \cr 1 &amp; 1 &amp; { - 1} \cr y &amp; {{x^2}} &amp; x \... GATE CE 1999 If$$A$$is any$$nxn$$matrix and$$k$$is a scalar then$$\left| {kA} \right| = \alpha \left| A \right|$$where$$\alp... GATE CE 1999 Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 &amp; -4 \cr 2 &amp; { 2 } \cr } } \ri... GATE CE 1998 The real symmetric matrix$$C$$corresponding to the quadratic form$$Q = 4{x_1}{x_2} - 5{x_2}{x_2}$$is GATE CE 1998 If$$A$$is a real square matrix then$$A{A^T}$$is GATE CE 1998 In matrix algebra$$AS=AT$$($$A,S,T,$$are matrices of appropriate order) implies$$S=T$$only if GATE CE 1998 If the determinant of the matrix$$\left[ {\matrix{ 1 &amp; 3 &amp; 2 \cr 0 &amp; 5 &amp; { - 6} \cr 2 &amp... GATE CE 1997 Inverse of matrix $$\left[ {\matrix{ 0 &amp; 1 &amp; 0 \cr 0 &amp; 0 &amp; 1 \cr 1 &amp; 0 &amp; 0 \cr ... GATE CE 1997 If$$A$$and$$B$$are two matrices and$$AB$$exists then$$BA$$exists, GATE CE 1997 Marks 2 More Consider the matrix$$\left[ {\matrix{ 5 &amp; { - 1} \cr 4 &amp; 1 \cr } } \right].$$Which one of the foll... GATE CE 2017 Set 1 If$$A = \left[ {\matrix{ 1 &amp; 5 \cr 6 &amp; 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 &amp; ... GATE CE 2017 Set 2 Consider the following linear system $$x+2y-3z=a$$$ $$2x+3y+3z=b$$$$$5x+9y-6z=c$$$ This system is consistent if $$a... GATE CE 2016 Set 2 The two Eigen Values of the matrix$$\left[ {\matrix{ 2 &amp; 1 \cr 1 &amp; p \cr } } \right]$$have a ratio... GATE CE 2015 Set 2 The smallest and largest Eigen values of the following matrix are :$$\left[ {\matrix{ 3 &amp; { - 2} &amp; 2 \cr ...
GATE CE 2015 Set 1
What is the minimum number of multiplications involved in computing the matrix product $$PQR?$$ Matrix $$P$$ has $$4$$ r...
GATE CE 2013
The inverse of the matrix $$\left[ {\matrix{ {3 + 2i} &amp; i \cr { - i} &amp; {3 - 2i} \cr } } \right]$$ is...
GATE CE 2010
For what values of $$\alpha$$ and $$\beta$$ the following simultaneous equations have an infinite number of solutions ...
GATE CE 2007
The minimum and maximum eigen values of matrix $$\left[ {\matrix{ 1 &amp; 1 &amp; 3 \cr 1 &amp; 5 &amp; 1 \cr ... GATE CE 2007 The inverse of$$2 \times 2$$matrix$$\left[ {\matrix{ 1 &amp; 2 \cr 5 &amp; 7 \cr } } \right]$$is GATE CE 2007 For a given matrix$$A = \left[ {\matrix{ 2 &amp; { - 2} &amp; 3 \cr { - 2} &amp; { - 1} &amp; 6 \cr 1 &amp...
GATE CE 2006

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