# Linear Algebra · Engineering Mathematics · GATE CE

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## Marks 1

GATE CE 2017 Set 2
Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$3{x_1} + 2{x_2} = {c_1}$$$$$4{x_1} + {x_2} = {c_2}... GATE CE 2017 Set 1 The matrix$$P$$is the inverse of a matrix$$Q.$$If$${\rm I}$$denotes the identity matrix, which one of the following options is correct? GATE CE 2016 Set 1 If the entries in each column of a square matrix$$M$$add up to$$1$$, then an eigenvalue of$$M$$is GATE CE 2015 Set 1 For what value of$$'p'$$the following set of equations will have no solutions?$$$2x+3y=5$3x+py=10$$GATE CE 2015 Set 2 Let$$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$with$$n \ge 3$$and$${{a_{ij}} = i.j.}$$The rank of$$A$$is : GATE CE 2014 Set 2 The determinant of matrix$$\left[ {\matrix{ 0 & 1 & 2 & 3 \cr 1 & 0 & 3 & 0 \cr 2 & 3 & 0 & 1 \cr ... GATE CE 2014 Set 2 The rank of the matrix $$\left[ {\matrix{ 6 & 0 & 4 & 4 \cr { - 2} & {14} & 8 & {18} \cr {14} & { - 14} &... GATE CE 2014 Set 1 Given the matrices$$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \cr } } \right]$$and$$K = ... GATE CE 2014 Set 1 The sum of Eigen values of the matrix, $$\left[ M \right]$$ is where $$\left[ M \right] = \left[ {\matrix{ {215} & {650} & {795} \cr ... GATE CE 2012 The eigen values of matrix$$\left[ {\matrix{ 9 & 5 \cr 5 & 8 \cr } } \right]$$are GATE CE 2009 A square matrix$$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,$4y-3z=12$$and$$$10x-2y+z...
GATE CE 2008
The product of matrices $${\left( {PQ} \right)^{ - 1}}P$$ is
GATE CE 2008
The eigenvalues of the matrix $$\left[ P \right] = \left[ {\matrix{ 4 & 5 \cr 2 & { - 5} \cr } } \right]$$ are
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 $$k$$ equal to GATE CE 2006 Solution for the system defined by the set of equations $$4y+3z=8, 2x-z=2$$ & $$3x+2y=5$$ is GATE CE 2005 Consider the following system of equations in three real variable $${x_1},$$ $${x_2}$$ and $${x_3}:$$ $$2{x_1} - {x_2} + 3{x_3} = 1$$$ $$3{x_1} + 2{... GATE CE 2005 Consider a non-homogeneous system of linear equations represents mathematically an over determined system. Such a system will be GATE CE 2005 Consider the matrices$$\,{X_{4x3,}}\,\,{Y_{4x3}}\,\,{P_{2x3}}.$$The order of$$\,{\left[ {P{{\left( {{X^T}Y} \right)}^{ - 1}}{P^T}} \right]^T}...
GATE CE 2005
Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda$$ is a scalar. Let $$\left( {{\lambda _i},\,\,... GATE CE 2004 Real matrices$$\,\,{\left[ A \right]_{3x1,}}\,\,{\left[ B \right]_{3x3,}}\,\,{\left[ C \right]_{3x5,}}\,\,{\left[ D \right]_{5x3,}}$$... GATE CE 2004 The eigen values of the matrix$$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$are GATE CE 2003 Given matrix$$\left[ A \right] = \left[ {\matrix{ 4 & 2 & 1 & 3 \cr 6 & 3 & 4 & 7 \cr 2 & 1 & 0 & 1 ...
GATE CE 2002
Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} & 4 \cr 4 & { - 1} \cr } } \right]$$
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 $$\left[ Q \right]\,$$ where $$\left... GATE CE 2001 The determinant of the following matrix$$\left[ {\matrix{ 5 & 3 & 2 \cr 1 & 2 & 6 \cr 3 & 5 & {10} \cr } } \...
GATE CE 2000
Consider the following two statements. $$(I)$$ The maximum number of linearly independent column vectors of a matrix $$A$$ is called the rank of $$A.... GATE CE 2000 If$$A,B,C$$are square matrices of the same order then$${\left( {ABC} \right)^{ - 1}}$$is equal be GATE CE 1999 If$$A$$is any$$nxn$$matrix and$$k$$is a scalar then$$\left| {kA} \right| = \alpha \left| A \right|$$where$$\alpha $$is GATE CE 1999 The equation$$\left[ {\matrix{ 2 & 1 & 1 \cr 1 & 1 & { - 1} \cr y & {{x^2}} & x \cr } } \right] = 0$$repres... GATE CE 1999 The number of terms in the expansion of general determinant of order$$n$$is GATE CE 1998 In matrix algebra$$AS=AT$$($$A,S,T,$$are matrices of appropriate order) implies$$S=T$$only if GATE CE 1998 If$$A$$is a real square matrix then$$A{A^T}$$is GATE CE 1998 The real symmetric matrix$$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].$$GATE CE 1997 If$$A$$and$$B$$are two matrices and$$AB$$exists then$$BA$$exists, GATE CE 1997 Inverse of matrix$$\left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 1 & 0 & 0 \cr } } \right]$$is GATE CE 1997 If the determinant of the matrix$$\left[ {\matrix{ 1 & 3 & 2 \cr 0 & 5 & { - 6} \cr 2 & 7 & 8 \cr } } \right...

## Marks 2

GATE CE 2017 Set 2
If $$A = \left[ {\matrix{ 1 & 5 \cr 6 & 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 & 7 \cr 8 & 4 \cr }... GATE CE 2017 Set 1 Consider the matrix$$\left[ {\matrix{ 5 & { - 1} \cr 4 & 1 \cr } } \right].$$Which one of the following statements is TRUE for t... GATE CE 2016 Set 2 Consider the following linear system$$$x+2y-3z=a$2x+3y+3z=b$5x+9y-6z=c$$This system is consistent if$$a,b$$and$$c$$satisfy the equ... GATE CE 2015 Set 1 The smallest and largest Eigen values of the following matrix are :$$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & { - 4} & 6 \cr... GATE CE 2015 Set 2 The two Eigen Values of the matrix $$\left[ {\matrix{ 2 & 1 \cr 1 & p \cr } } \right]$$ have a ratio of $$3:1$$ for $$p=2.$$ What ... GATE CE 2013 What is the minimum number of multiplications involved in computing the matrix product $$PQR?$$ Matrix $$P$$ has $$4$$ rows and $$2$$ columns, matrix ... GATE CE 2010 The inverse of the matrix $$\left[ {\matrix{ {3 + 2i} & i \cr { - i} & {3 - 2i} \cr } } \right]$$ is GATE CE 2007 The inverse of $$2 \times 2$$ matrix $$\left[ {\matrix{ 1 & 2 \cr 5 & 7 \cr } } \right]$$ is GATE CE 2007 The minimum and maximum eigen values of matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr }... GATE CE 2007 For what values of$$\alpha $$and$$\beta $$the following simultaneous equations have an infinite number of solutions$$$x+y+z=5,$x+3y+3z=9,$...
GATE CE 2006
For a given matrix A = \left[ {\matrix{ 2 & { - 2} & 3 \cr { - 2} & { - 1} & 6 \cr 1 & 2 & 0 \cr } } \right...
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