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Previous Years Questions

Marks 1

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If $$V$$ is a non-zero vector of dimension $$3 \times 1,$$ then the matrix $$\,A = V{V^T}$$ has a rank $$=$$ ________
GATE IN 2017
The eigen values of the matrix $$A = \left[ {\matrix{ 1 & { - 1} & 5 \cr 0 & 5 & 6 \cr 0 &a...
GATE IN 2017
The figure shows a shape $$ABC$$ and its minor image $${A_1}$$$${B_1}$$$${C_1}$$ across the horizontal axis ($$x$$-axis...
GATE IN 2017
Let $$A$$ be an $$n \times n$$ matrix with rank $$r\left( {0 < r < n} \right).$$ Then $$AX=0$$ has $$p$$ independe...
GATE IN 2015
For the matrix $$A$$ satisfying the equation given below, the eigen values are $$$\left[ A \right]\left[ {\matrix{ ...
GATE IN 2014
A scalar valued function is defined as $$f\left( x \right){x^T}Ax + {b^T}x + c,$$ where $$A$$ is a symmetric positive de...
GATE IN 2014
The dimension of the null space of the matrix $$\left[ {\matrix{ 0 & 1 & 1 \cr 1 & { - 1} & 0 \...
GATE IN 2013
Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[...
GATE IN 2012
The matrix $$M = \left[ {\matrix{ { - 2} & 2 & { - 3} \cr 2 & 1 & 6 \cr { - 1} & { - 2}...
GATE IN 2011
A real $$n \times n$$ matrix $$A$$ $$ = \left[ {{a_{ij}}} \right]$$ is defined as follows $$\left\{ {\matrix{ {{a_{i...
GATE IN 2010
$$X$$ and $$Y$$ are non-zero square matrices of size $$n \times n$$. If $$XY = {O_{n \times n}}$$ then
GATE IN 2010
The eigen values of a $$2 \times 2$$ matrix $$X$$ are $$-2$$ and $$-3$$. The eigen values of matrix $${\left( {X + 1} \r...
GATE IN 2009
Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and $${{a_{ij}} = i.j.}$$ Then the rank of $...
GATE IN 2007
Let $$A$$ be $$3 \times 3$$ matrix with rank $$2.$$ Then $$AX=O$$ has
GATE IN 2005
Identity which one of the following is an eigen vectors of the matrix $$A = \left[ {\matrix{ 1 & 0 \cr { - 1...
GATE IN 2005
The necessary condition to diagonalize a matrix is that
GATE IN 2001
The rank of matrix $$A = \left[ {\matrix{ 1 & 2 & 3 \cr 3 & 4 & 5 \cr 4 & 6 & 8 \c...
GATE IN 2000

Marks 2

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Consider the matrix $$A = \left( {\matrix{ 2 & 1 & 1 \cr 2 & 3 & 4 \cr { - 1} & { - 1} ...
GATE IN 2016
One pair of eigenvectors corresponding to the two eigen values of the matrix $$\left[ {\matrix{ 0 & { - 1} \cr ...
GATE IN 2013
Let $$A$$ be $$n \times n$$ real matrix such that $${A^2} = {\rm I}$$ and $$Y$$ be an $$n$$-diamensional vector. Then th...
GATE IN 2007
A system of linear simultaneous equations is given as $$AX=b$$ where $$A = \left[ {\matrix{ 1 & 0 & 1 & ...
GATE IN 2006
A system of linear simultaneous equations is given as $$AX=b$$ where $$A = \left[ {\matrix{ 1 & 0 & 1 & ...
GATE IN 2006
For a given $$2x2$$ matrix $$A,$$ it is observved that $$A\left[ {\matrix{ 1 \cr { - 1} \cr } } \right] = -...
GATE IN 2006

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