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## Marks 1

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Consider a matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 2} \cr 0 & 1 & 1 \cr } } \right]$$. ...
GATE EE 2022
e4 denotes the exponential of a square matrix A. Suppose $$\lambda$$ is an eigen value and v is the corresponding eigen-...
GATE EE 2022
Consider a 3 $$\times$$ 3 matrix A whose (i, j)-th element, ai,j = (i $$-$$ j)3. Then the matrix A will be...
GATE EE 2022
The matrix $$A = \left[ {\matrix{ {{3 \over 2}} &amp; 0 &amp; {{1 \over 2}} \cr 0 &amp; { - 1} &amp; 0 \cr ... GATE EE 2017 Set 1$$A3 \times 3$$matrix$$P$$is such that ,$${p^3} = P.$$Then the eigen values of$$P$$are GATE EE 2016 Set 2 Consider$$3 \times 3$$matrix with every element being equal to$$1.$$Its only non-zero eigenvalue is __________. GATE EE 2016 Set 1 If the sum of the diagonal elements of a$$2 \times 2$$matrix is$$-6$$, then the maximum possible value of determinant... GATE EE 2015 Set 1 We have a set of$$3$$linear equations in$$3$$unknown.$$'X \equiv Y'$$means$$X$$and$$Y$$are equivalent statemen... GATE EE 2015 Set 2 Which one of the following statements is true for all real symmetric matrices? GATE EE 2014 Set 2 Given a system of equations$$$x + 2y + 2z = {b_1}$5x + y + 3z = {b_2}$$Which of the following is true its solu... GATE EE 2014 Set 1 Given that$$A = \left[ {\matrix{ { - 5} &amp; { - 3} \cr 2 &amp; 0 \cr } } \right]$$and$${\rm I} = \left[...
GATE EE 2012
An eigen vector of $$p = \left[ {\matrix{ 1 &amp; 1 &amp; 0 \cr 0 &amp; 2 &amp; 2 \cr 0 &amp; 0 &amp; 3 \c... GATE EE 2010 The trace and determinant of a$$2 \times 2$$matrix are shown to be$$-2$$and$$-35$$respectively. Its eigen values a... GATE EE 2009$$A$$is$$mxn$$full rank matrix with$$m &gt; n$$and$${\rm I}$$is an identity matrix. Let matrix$${A^ + ...
GATE EE 2008
The characteristic equation of a $$3\,\, \times \,\,3$$ matrix $$P$$ is defined as $$\alpha \left( \lambda \right) = \... GATE EE 2008$$X = {\left[ {\matrix{ {{x_1}} &amp; {{x_2}} &amp; {.......\,{x_n}} \cr } } \right]^T}$$is an$$n$$-tuple non- ... GATE EE 2007 In the matrix equation$$PX=Q$$which of the following is a necessary condition for the existence of atleast one solutio... GATE EE 2005 The determinant of the matrix$$\left[ {\matrix{ 1 &amp; 0 &amp; 0 &amp; 0 \cr {100} &amp; 1 &amp; 0 &amp; 0 \c...
GATE EE 2002
Find the eigen values and eigen vectors of the matrix $$\left[ {\matrix{ 3 &amp; { - 1} \cr { - 1} &amp; 3 \cr ... GATE EE 1999 If$$A = \left[ {\matrix{ 1 &amp; { - 2} &amp; { - 1} \cr 2 &amp; 3 &amp; 1 \cr 0 &amp; 5 &amp; { - 2} \cr...
GATE EE 1999
If $$A = \left[ {\matrix{ 5 &amp; 0 &amp; 2 \cr 0 &amp; 3 &amp; 0 \cr 2 &amp; 0 &amp; 1 \cr } } \right]... GATE EE 1998 If the vector$$\left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right]$$is an eigen vector of$$A = \left...
GATE EE 1998
A set of linear equations is represented by the matrix equations $$Ax=b.$$ The necessary condition for the existence of ...
GATE EE 1998
$$A = \left[ {\matrix{ 2 &amp; 0 &amp; 0 &amp; { - 1} \cr 0 &amp; 1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 3 &... GATE EE 1998 Express the given matrix$$A = \left[ {\matrix{ 2 &amp; 1 &amp; 5 \cr 4 &amp; 8 &amp; {13} \cr 6 &amp; {27}...
GATE EE 1997
The rank of the following $$(n+1)$$ $$x$$ $$(n+1)$$ matrix, where $$'a'$$ is a real number is $$\left[ {\matrix{ 1 ... GATE EE 1995 Given the matrix$$A = \left[ {\matrix{ 0 &amp; 1 &amp; 0 \cr 0 &amp; 0 &amp; 1 \cr { - 6} &amp; { - 11} &a...
GATE EE 1995
The inverse of the matrix $$S = \left[ {\matrix{ 1 &amp; { - 1} &amp; 0 \cr 1 &amp; 1 &amp; 1 \cr 0 &amp; 0... GATE EE 1995 The number of linearly independent solutions of the system of equations$$\left[ {\matrix{ 1 &amp; 0 &amp; 2 \cr ...
GATE EE 1994
$$A$$ $$\,\,5 \times 7$$ matrix has all its entries equal to $$1.$$ Then the rank of a matrix is
GATE EE 1994
The eigen values of the matrix $$\left[ {\matrix{ a &amp; 1 \cr a &amp; 1 \cr } } \right]$$ are
GATE EE 1994

## Marks 2

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The eigen values of the matrix given below are $$\left[ {\matrix{ 0 &amp; 1 &amp; 0 \cr 0 &amp; 0 &amp; 1 \cr ... GATE EE 2017 Set 2 Let$$P = \left[ {\matrix{ 3 &amp; 1 \cr 1 &amp; 3 \cr } } \right].$$Consider the set$$S$$of all vectors ... GATE EE 2016 Set 2 Let the eigenvalues of a$$2 \times 2$$matrix$$A$$be$$1,-2$$with eigenvectors$${x_1}$$and$${x_2}$$respectively.... GATE EE 2016 Set 1 Let$$A$$be a$$4 \times 3$$real matrix which rank$$2.$$Which one of the following statement is TRUE? GATE EE 2016 Set 1 The maximum value of$$'a'$$such that the matrix$$\left[ {\matrix{ { - 3} &amp; 0 &amp; { - 2} \cr 1 &amp; { -...
GATE EE 2015 Set 1
$$A = \left[ {\matrix{ p &amp; q \cr r &amp; s \cr } } \right];B = \left[ {\matrix{ {{p^2} + {q^2}} &amp;... GATE EE 2014 Set 3 A system matrix is given as follows$$$A = \left[ {\matrix{ 0 &amp; 1 &amp; { - 1} \cr { - 6} &amp; { - 11} &am... GATE EE 2014 Set 1 A matrix has eigen values $$-1$$ and $$-2.$$ The corresponding eigenvectors are $$\left[ {\matrix{ 1 \cr { - 1} ... GATE EE 2013 The equation$$\left[ {\matrix{ 2 &amp; { - 2} \cr 1 &amp; { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}}... GATE EE 2013 The matrix $$\left[ A \right] = \left[ {\matrix{ 2 &amp; 1 \cr 4 &amp; { - 1} \cr } } \right]$$ is decompose... GATE EE 2011 The two vectors $$\left[ {\matrix{ 1 &amp; 1 &amp; 1 \cr } } \right]$$ and $$\left[ {\matrix{ 1 &amp; a &amp; ... GATE EE 2011 For the set of equations$$${x_1} + 2{x_2} + {x_3} + 4{x_4} = 2,\$3{x_1} + 6{x_2} + 3{x_3} + 12{x_4} = 6.$$The f... GATE EE 2010 Let$$P$$be$$2x2$$real orthogonal matrix and$$\overline x $$is a real vector$${\left[ {\matrix{ {{x_1}} &amp; {...
GATE EE 2008
If the rank of a $$5x6$$ matrix $$Q$$ is $$4$$ then which one of the following statements is correct?
GATE EE 2008
Let $$x$$ and $$y$$ be two vectors in a $$3-$$ dimensional space and $$&lt; x,y &gt;$$ denote their dot product. Then ...
GATE EE 2007
If $$A = \left[ {\matrix{ { - 3} &amp; 2 \cr { - 1} &amp; 0 \cr } } \right]$$ then $$A$$ satisfies the rela...
GATE EE 2007
If $$A = \left[ {\matrix{ { - 3} &amp; 2 \cr { - 1} &amp; 0 \cr } } \right]\,$$ then $${A^9}$$ equals
GATE EE 2007
$${q_1},\,{q_2},{q_3},.......{q_m}$$ are $$n$$-dimensional vectors with $$m &lt; n.$$ This set of vectors is linearly de...
GATE EE 2007
If $$R = \left[ {\matrix{ 1 &amp; 0 &amp; { - 1} \cr 2 &amp; 1 &amp; { - 1} \cr 2 &amp; 3 &amp; 2 \cr }... GATE EE 2005 For the matrix$$P = \left[ {\matrix{ 3 &amp; { - 2} &amp; 2 \cr 0 &amp; { - 2} &amp; 1 \cr 0 &amp; 0 &amp;...
GATE EE 2005

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