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Which of the following is/are the eigen vector(s) for the matrix given below? $$\left( {\matrix{ { - 9} & { - 6} & { ... GATE CSE 2022 Consider solving the following system of simultaneous equations using LU decomposition. x1 + x2$$-$$2x3 = 4 x1 + 3x2 ... GATE CSE 2022 Which one of the following is the closed form for the generating function of the sequence (an}n$$\ge$$0 defined below?... GATE CSE 2022 Consider the following two statements with respect to the matrices Am$$\times$$n , Bn$$\times$$m , Cn$$\times$$n a... GATE CSE 2022 Let X be a square matrix. Consider the following two statements on X. I. X is invertible. II. Determinant of X is non-z... GATE CSE 2019 Consider a matrix$$A = u{v^T}$$where$$u = \left( {\matrix{ 1 \cr 2 \cr } } \right),v = \left( {\matrix{ ...
GATE CSE 2018
Let $${c_1},.....,\,\,{c_n}$$ be scalars, not all zero, such that $$\sum\limits_{i = 1}^n {{c_i}{a_i} = 0}$$ where $${{... GATE CSE 2017 Set 1 Let$$P = \left[ {\matrix{ 1 &amp; 1 &amp; { - 1} \cr 2 &amp; { - 3} &amp; 4 \cr 3 &amp; { - 2} &amp; 3 \c...
GATE CSE 2017 Set 2
Let $${a_n}$$ be the number of $$n$$-bit strings that do NOT contain two consecutive $$1s.$$ Which one of the following ...
GATE CSE 2016 Set 1
Suppose that the eigen values of matrix $$A$$ are $$1, 2, 4.$$ The determinant of $${\left( {{A^{ - 1}}} \right)^T}$$ is...
GATE CSE 2016 Set 2
Consider the system, each consisting of m linear equations in $$n$$ variables. $$I.$$ $$\,\,\,$$ If $$m &lt; n,$$ then ...
GATE CSE 2016 Set 2
Two eigenvalues of a $$3 \times 3$$ real matrix $$P$$ are $$\left( {2 + \sqrt { - 1} } \right)$$ and $$3.$$ The determin...
GATE CSE 2016 Set 1
The number of divisors of $$2100$$ is ___________.
GATE CSE 2015 Set 2
In the LU decomposition of the matrix $$\left[ {\matrix{ 2 &amp; 2 \cr 4 &amp; 9 \cr } } \right]$$, if the d...
GATE CSE 2015 Set 1
The larger of the two eigenvalues of the matrix $$\left[ {\matrix{ 4 &amp; 5 \cr 2 &amp; 1 \cr } } \right]$$...
GATE CSE 2015 Set 2
In the given matrix $$\left[ {\matrix{ 1 &amp; { - 1} &amp; 2 \cr 0 &amp; 1 &amp; 0 \cr 1 &amp; 2 &amp; 1 ... GATE CSE 2015 Set 3 If$${V_1}$$and$${V_2}$$are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dim... GATE CSE 2014 Set 3 Which one of the following statements is TRUE about every$$n\,\, \times \,n$$matrix with only real eigen values? GATE CSE 2014 Set 3 Consider the following system of equations: 3x + 2y = 1 4x + 7z = 1 x + y + z =3 x - 2y + 7z = 0 The number of solu... GATE CSE 2014 Set 1 If the matrix A is such that$$$A = \left[ {\matrix{ 2 \cr { - 4} \cr 7 \cr } } \right]\,\,\left[ {\ma... GATE CSE 2014 Set 2 The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4-by-4 symmetr... GATE CSE 2014 Set 1 Which of the following does not equal $$\left| {\matrix{ 1 &amp; x &amp; {{x^2}} \cr 1 &amp; y &amp; {{y^2}} \... GATE CSE 2013 Let$$A$$be the$$2 \times 2$$matrix with elements$${a_{11}} = {a_{12}} = {a_{21}} = + 1$$and$${a_{22}} = - 1$$. ... GATE CSE 2012 Consider the following matrix$$A = \left[ {\matrix{ 2 &amp; 3 \cr x &amp; y \cr } } \right].$$If the eige... GATE CSE 2010 The following system of equations$${x_1}\, + \,{x_2}\, + 2{x_3}\, = 1{x_1}\, + \,2 {x_2}\, + 3{x_3}\, = 2{... GATE CSE 2008 Let $$A$$ be the matrix $$\left[ {\matrix{ 3 &amp; 1 \cr 1 &amp; 2 \cr } } \right]$$. What is the maximum v... GATE CSE 2007 The determination of the matrix given below is $$\left[ {\matrix{ 0 &amp; 1 &amp; 0 &amp; 2 \cr { - 1} &amp; 1 ... GATE CSE 2005 The number of different$$n \times n$$symmetric matrices with each elements being either$$0$$or$$1$$is GATE CSE 2004 What values of x, y and z satisfy the following system of linear equations?$$$\left[ {\matrix{ 1 &amp; 2 &amp; 3 \c...
GATE CSE 2004
Let A, B, C, D be $$n\,\, \times \,\,n$$ matrices, each with non-zero determination. If ABCD = I, then $${B^{ - 1}}$$ is...
GATE CSE 2004
$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix...
GATE CSE 2003
The rank of the matrix$$\left[ {\matrix{ 1 &amp; 1 \cr 0 &amp; 0 \cr } } \right]\,\,is$$
GATE CSE 2002
Consider the following statements: S1: The sum of two singular n x n matrices may be non-singular S2: The sum of two n...
GATE CSE 2001
An $$n\,\, \times \,\,n$$ array v is defined as follows v[i, j] = i - j for all i, j, $$1\,\, \le \,\,i\,\, \le \,\,n,\,... GATE CSE 2000 The determinant of the matrix$$$\left[ {\matrix{ 2 &amp; 0 &amp; 0 &amp; 0 \cr 8 &amp; 1 &amp; 7 &amp; 2 \cr ... GATE CSE 2000 Consider the following set a equations x + 2y = 5 4x + 8y = 12 3x + 6y + 3z = 15 This set GATE CSE 1998 The determination of the matrix $$\left[ {\matrix{ 6 &amp; { - 8} &amp; 1 &amp; 1 \cr 0 &amp; 2 &amp; 4 &amp; 6... GATE CSE 1997 Let$$A = \left[ {\matrix{ {{a_{11}}} &amp; {{a_{12}}} \cr {{a_{21}}} &amp; {{a_{22}}} \cr } } \right]\,\,$$... GATE CSE 1996 Let AX = B be a system of linear equations where A is an m x n matrix and B is a$$m\,\, \times \,\,1$$column vector an... GATE CSE 1996 The rank of the following (n + 1) x (n + 1) matrix, where a is a real number is$$$\left[ {\matrix{ 1 &amp; a &amp; ...
GATE CSE 1995
The rank of the following (n + 1) x (n + 1) matrix, where a is a real number is $$\left[ {\matrix{ 1 &amp; a &amp; ... GATE CSE 1995 The rank of the matrix$$\left[ {\matrix{ 0 &amp; 0 &amp; { - 3} \cr 9 &amp; 3 &amp; 5 \cr 3 &amp; 1 &amp; ...
GATE CSE 1994
The inverse of the matrix $$\left[ {\matrix{ 1 &amp; 0 &amp; 1 \cr { - 1} &amp; 1 &amp; 1 \cr 0 &amp; 1 &am... GATE CSE 1994 If$$A = \left[ {\matrix{ 1 &amp; 0 &amp; 0 &amp; 1 \cr 0 &amp; { - 1} &amp; 0 &amp; { - 1} \cr 0 &amp; 0 &...
GATE CSE 1993
The eigen vector (s) of the matrix $$\left[ {\matrix{ 0 &amp; 0 &amp; \alpha \cr 0 &amp; 0 &amp; 0 \cr 0 ... GATE CSE 1993 ## Marks 2 More Consider the following matrix.$$\left( {\begin{array}{*{20}{c}} 0&amp;1&amp;1&amp;1\\ 1&amp;0&amp;1&amp;1\\ 1&amp;1&am...
GATE CSE 2021 Set 1
Let A and B be two n$$\times$$n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of ...
GATE CSE 2020
Consider a matrix P whose only eigenvectors are the multiples of $$\left[ {\matrix{ 1 \cr 4 \cr } } \right]... GATE CSE 2018 Which one of the following is a closed form expression for the generating function of the sequence$$\left\{ {{a_n}} \ri...
GATE CSE 2018
Let $$A$$ be $$n\,\, \times \,\,n$$ real valued square symmetric matrix of rank $$2$$ with $$\sum\limits_{i = 1}^n {\sum... GATE CSE 2017 Set 1 If the characteristic polynomial of a$$3 \times 3$$matrix$$M$$over$$R$$(the set of real numbers) is$${\lambda ^3} ...
GATE CSE 2017 Set 2
The value of the expression $${13^{99}}$$ ($$mod$$ $$17$$), in the range $$0$$ to $$16,$$ is ______________ .
GATE CSE 2016 Set 2
Consider the recurrence relation $${a_1} = 8,\,{a_n} = 6{n^2} + 2n + {a_{n - 1}}.$$ Let $${a_{99}} = K \times {10^4}.$$...
GATE CSE 2016 Set 1
Let $${A_1},\,{A_2},\,{A_3}$$ and $${A_4}$$ be four matrices of dimensions $$10 \times 5,\,5 \times 20,\,20 \times 10,$$...
GATE CSE 2016 Set 2
Let $${a_n}$$ represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence rela...
GATE CSE 2015 Set 1
$$\sum\limits_{x = 1}^{99} {{1 \over {x\left( {x + 1} \right)}}}$$ = _____________.
GATE CSE 2015 Set 1
If the following system has non - trivial solution $$px+qy+rz=0$$$$$qx+ry+pz=0$$$ $$rx+py+qz=0$$$Then which one of... GATE CSE 2015 Set 3 Perform the following operations on the matrix $$\left[ {\matrix{ 3 &amp; 4 &amp; {45} \cr 7 &amp; 9 &amp; {105}... GATE CSE 2015 Set 2 Consider the following$$2 \times 2$$matrix$$A$$where two elements are unknown and are marked by$$a$$and$$b.$$The... GATE CSE 2015 Set 1 The product of the non-zero eigenvalues of the matrix$$\left[ {\matrix{ 1 &amp; 0 &amp; 0 &amp; 0 &amp; 1 \cr ... GATE CSE 2014 Set 2 $$\left[ A \right]$$ is a square matrix which is neither symmetric nor skew-symmetric and $${\left[ A \right]^T}$$ is it... GATE CSE 2011 Consider the matrix as given below. $$\left[ {\matrix{ 1 &amp; 2 &amp; 3 \cr 0 &amp; 4 &amp; 7 \cr 0 &amp... GATE CSE 2011 Four matrices$${M_1},\,\,\,{M_2},\,\,\,{M_3}$$and$${M_4}$$of dimensions$$p\,\,x\,\,q,\,\,\,\,\,q\,\,x\,\,e,\,\,\,\,... GATE CSE 2011 Consider the following matrix $$A = \left[ {\matrix{ 2 &amp; 3 \cr x &amp; y \cr } } \right]\,\,$$ If the ei... GATE CSE 2010 If $$M$$ is a square matrix with a zero determinant, which of the following assertion(s) is (are) correct? $$S1$$ : Eac... GATE CSE 2008 How many of the following matrices have an eigen value $$1$$? $$\left[ {\matrix{ 1 &amp; 0 \cr 0 &amp; 0 \cr ... GATE CSE 2008 Let$$A$$be$$a4x4$$matrix with eigen values$$-5$$,$$-2, 1, 4$$. Which of the following is an eigen ... GATE CSE 2007 What are the eigen values of the matrix$$P$$given below?$$$P = \left( {\matrix{ a &amp; 1 &amp; 0 \cr 1 &amp;...
GATE CSE 2006
$$F$$ is an $$n$$ $$x$$ $$n$$ real matrix. $$b$$ is an $$n$$ $$x$$ $$1$$ real vector. Suppose there are two $$n$$ $$x$$ ...
GATE CSE 2006
Consider the following system of equations in three real variables $$x1, x2$$ and $$x3$$ : $$2x1 - x2 + 3x3 = 1$$ $$3x1 ... GATE CSE 2005 What are the eigen values of the following$$2x2$$matrix?$$$\left[ {\matrix{ 2 &amp; { - 1} \cr { - 4} &amp; 5... GATE CSE 2005 Consider the set $$H$$ of all $$3$$ $$X$$ $$3$$ matrices of the type $$\left[ {\matrix{ a &amp; f &amp; e \cr 0... GATE CSE 2005 In an M$$ \times $$N matrix such that all non-zero entries are covered in$$a$$rows and$$b$$columns. Then the maximum... GATE CSE 2004 If matrix$$X = \left[ {\matrix{ a &amp; 1 \cr { - {a^2} + a - 1} &amp; {1 - a} \cr } } \right]$$and$${X^... GATE CSE 2004 Let $$A$$ be and n$$\times$$n matrix of the folowing form. What is the value of the determinant of $$A$$?... GATE CSE 2004 How many solutions does the following system of linear equations have? - x + 5y = - 1x - y = 2x + 3y = 3 ... GATE CSE 2004 Consider the following system of linear equations $$\left[ {\matrix{ 2 &amp; 1 &amp; { - 4} \cr 4 &amp; 3 &amp... GATE CSE 2003 Obtain the eigen values of the matrix$$$A = \left[ {\matrix{ 1 &amp; 2 &amp; {34} &amp; {49} \cr 0 &amp; 2 &amp...
GATE CSE 2002
Consider the following determinant $$\Delta = \left| {\matrix{ 1 &amp; a &amp; {bc} \cr 1 &amp; a &amp; {ca} ... GATE CSE 1998 The rank of the matrix given below is:$$$\left[ {\matrix{ 1 &amp; 4 &amp; 8 &amp; 7 \cr 0 &amp; 0 &amp; 3 &amp;... GATE CSE 1998 Let $$A = ({a_{ij}})$$ be and n-rowed square matrix and $${I_{12}}$$ be the matrix obtained by interchanging the first a... GATE CSE 1997 The matrices$\$\left[ {\matrix{ {\cos \,\theta } &amp; { - \sin \,\theta } \cr {\sin \,\,\theta } &amp; {\cos \,\...
GATE CSE 1996
In a compact single dimensional array representation for lower triangular matrices (i.e., all the elements above the dia...
GATE CSE 1994
If A and B are real symmetric matrices of size n x n. Then, which one of the following is true?
GATE CSE 1994
If a, b and c are constants, which of the following is a linear inequality?
GATE CSE 1987
A square matrix is singular whenever:
GATE CSE 1987

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