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Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$3{x_1} + 2{x_2} = {c_1... GATE CE 2017 Set 2 The matrix$$P$$is the inverse of a matrix$$Q.$$If$${\rm I}$$denotes the identity matrix, which one of the followin... GATE CE 2017 Set 1 If the entries in each column of a square matrix$$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$$GATE CE 2015 Set 1 The determinant of matrix$$\left[ {\matrix{ 0 & 1 & 2 & 3 \cr 1 & 0 & 3 & 0 \cr 2 & 3 & 0 & 1 \cr 3 &...
GATE CE 2014 Set 2
The rank of the matrix $$\left[ {\matrix{ 6 & 0 & 4 & 4 \cr { - 2} & {14} & 8 & {18} \cr {14} & { - 14} & 0... GATE CE 2014 Set 2 Given the matrices$$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \cr } } \right]$$and ... GATE CE 2014 Set 1 The sum of Eigen values of the matrix,$$\left[ M \right]$$is where$$\left[ M \right] = \left[ {\matrix{ {215} & {...
GATE CE 2014 Set 1
The eigen values of matrix $$\left[ {\matrix{ 9 & 5 \cr 5 & 8 \cr } } \right]$$ are
GATE CE 2012
A square matrix $$B$$ is symmetric if ____
GATE CE 2009
In the solution of the following set of linear equations by Gauss-elimination using partial pivoting $$5x+y+2z=34,$$$... GATE CE 2009 The product of matrices $${\left( {PQ} \right)^{ - 1}}P$$ is GATE CE 2008 The eigenvalues of the matrix $$\left[ P \right] = \left[ {\matrix{ 4 & 5 \cr 2 & { - 5} \cr } } \right]$$ a... GATE CE 2008 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 Solution for the system defined by the set of equations $$4y+3z=8, 2x-z=2$$ & $$3x+2y=5$$ is GATE CE 2006 Consider the following system of equations in three real variable $${x_1},$$ $${x_2}$$ and $${x_3}:$$ $$2{x_1} - {x_2} ... GATE CE 2005 Consider a non-homogeneous system of linear equations represents mathematically an over determined system. Such a system... GATE CE 2005 Consider the matrices$$\,{X_{4x3,}}\,\,{Y_{4x3}}\,\,{P_{2x3}}.$$The order of$$\,{\left[ {P{{\left( {{X^T}Y} \ri... GATE CE 2005 Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda$$ is a scalar. L... GATE CE 2005 Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\... GATE CE 2004 The eigen values of the matrix$$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$are GATE CE 2004 Given matrix$$\left[ A \right] = \left[ {\matrix{ 4 & 2 & 1 & 3 \cr 6 & 3 & 4 & 7 \cr 2 & 1 & 0 & 1 \cr ... GATE CE 2003 Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} & 4 \cr 4 & { - 1} \cr } } \right]$$ GATE CE 2002 The determinant of the following matrix $$\left[ {\matrix{ 5 & 3 & 2 \cr 1 & 2 & 6 \cr 3 & 5 & {10} \cr ... GATE CE 2001 The eigen values of the matrix$$\left[ {\matrix{ 5 & 3 \cr 2 & 9 \cr } } \right]$$are GATE CE 2001 The product$$\left[ P \right]\,\,{\left[ Q \right]^T}$$of the following two matrices$$\left[ P \right]\,$$and$$\lef... GATE CE 2001 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 $$... GATE CE 2000 If$$A$$is any$$nxn$$matrix and$$k$$is a scalar then$$\left| {kA} \right| = \alpha \left| A \right|$$where$$\alp... GATE CE 1999 The number of terms in the expansion of general determinant of order $$n$$ is GATE CE 1999 The equation $$\left[ {\matrix{ 2 & 1 & 1 \cr 1 & 1 & { - 1} \cr y & {{x^2}} & x \cr } } \right] = 0$$ ... GATE CE 1999 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 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 Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 & -4 \cr 2 & { 2 } \cr } } \right].$$ GATE CE 1998 Inverse of matrix $$\left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 1 & 0 & 0 \cr } } \right]$$ is GATE CE 1997 If $$A$$ and $$B$$ are two matrices and $$AB$$ exists then $$BA$$ exists, GATE CE 1997 If the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 2 \cr 0 & 5 & { - 6} \cr 2 & 7 & 8 \cr } } ... GATE CE 1997 Marks 2 More If$$A = \left[ {\matrix{ 1 & 5 \cr 6 & 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 & 7 \cr 8... GATE CE 2017 Set 2 Consider the matrix $$\left[ {\matrix{ 5 & { - 1} \cr 4 & 1 \cr } } \right].$$ Which one of the following st... GATE CE 2017 Set 1 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 & 1 \cr 1 & p \cr } } \right]$$have a ratio of$$3:...
GATE CE 2015 Set 2
The smallest and largest Eigen values of the following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & {... GATE CE 2015 Set 1 What is the minimum number of multiplications involved in computing the matrix product$$PQR?$$Matrix$$P$$has$$4$$r... GATE CE 2013 The inverse of the matrix$$\left[ {\matrix{ {3 + 2i} & i \cr { - i} & {3 - 2i} \cr } } \right]$$is GATE CE 2010 The inverse of$$2 \times 2$$matrix$$\left[ {\matrix{ 1 & 2 \cr 5 & 7 \cr } } \right]$$is GATE CE 2007 For what values of$$\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 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \c...
GATE CE 2007
For a given matrix A = \left[ {\matrix{ 2 & { - 2} & 3 \cr { - 2} & { - 1} & 6 \cr 1 & 2 & 0 \cr } } ...
GATE CE 2006

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