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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 $$A = \left[ {\matrix{ 1 &amp; { - 1} &amp; 5 \cr 0 &amp; 5 &amp; 6 \cr 0 &a... GATE IN 2017 The figure shows a shape$$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 &lt; r &lt; 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 $$\left[ {\matrix{ 0 &amp; 1 &amp; 1 \cr 1 &amp; { - 1} &amp; 0 \... GATE IN 2013 Given that$$A = \left[ {\matrix{ { - 5} &amp; { - 3} \cr 2 &amp; 0 \cr } } \right]$$and$${\rm I} = \left[...
GATE IN 2012
The matrix $$M = \left[ {\matrix{ { - 2} &amp; 2 &amp; { - 3} \cr 2 &amp; 1 &amp; 6 \cr { - 1} &amp; { - 2}... GATE IN 2011 A real$$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 &amp; 0 \cr { - 1...
GATE IN 2005
The necessary condition to diagonalize a matrix is that
GATE IN 2001
The rank of matrix $$A = \left[ {\matrix{ 1 &amp; 2 &amp; 3 \cr 3 &amp; 4 &amp; 5 \cr 4 &amp; 6 &amp; 8 \c... GATE IN 2000 ## Marks 2 More Consider the matrix$$A = \left( {\matrix{ 2 &amp; 1 &amp; 1 \cr 2 &amp; 3 &amp; 4 \cr { - 1} &amp; { - 1} ...
GATE IN 2016
One pair of eigenvectors corresponding to the two eigen values of the matrix $$\left[ {\matrix{ 0 &amp; { - 1} \cr ... GATE IN 2013 Let$$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 &amp; 0 &amp; 1 &amp; ...
GATE IN 2006
A system of linear simultaneous equations is given as $$AX=b$$ where $$A = \left[ {\matrix{ 1 &amp; 0 &amp; 1 &amp; ... GATE IN 2006 For a given$$2x2$$matrix$$A,$$it is observved that$$A\left[ {\matrix{ 1 \cr { - 1} \cr } } \right] = -...
GATE IN 2006

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