## Marks 1

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The matrix $$A = \left[ {\matrix{ {{3 \over 2}} & 0 & {{1 \over 2}} \cr 0 & { - 1} & 0 \cr {{1 \over 2}} & ... GATE EE 2017 Set 1$$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.$$Its only non-zero eigenvalue is __________. GATE EE 2016 Set 1 We have a set of$$3$$linear equations in$$3$$unknown.$$'X \equiv Y'$$means$$X$$and$$Y$$are equivalent statemen... GATE EE 2015 Set 2 If the sum of the diagonal elements of a$$2 \times 2$$matrix is$$-6$$, then the maximum possible value of determinant... GATE EE 2015 Set 1 Which one of the following statements is true for all real symmetric matrices? GATE EE 2014 Set 2 Given a system of equations$$$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} & { - 3} \cr 2 & 0 \cr } } \right]$$and$${\rm I} = \left[ {\matri...
GATE EE 2012
An eigen vector of $$p = \left[ {\matrix{ 1 & 1 & 0 \cr 0 & 2 & 2 \cr 0 & 0 & 3 \cr } } \right]$$ is
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
The characteristic equation of a $$3\,\, \times \,\,3$$ matrix $$P$$ is defined as $$\alpha \left( \lambda \right) = \... GATE EE 2008$$A$$is$$mxn$$full rank matrix with$$m > n$$and$${\rm I}$$is an identity matrix. Let matrix$${A^ + } =...
GATE EE 2008
$$X = {\left[ {\matrix{ {{x_1}} & {{x_2}} & {.......\,{x_n}} \cr } } \right]^T}$$ is an $$n$$-tuple non- zero vec...
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 $$\left[ {\matrix{ 1 & 0 & 0 & 0 \cr {100} & 1 & 0 & 0 \cr {100} & {200} & 1 ... GATE EE 2002 If$$A = \left[ {\matrix{ 1 & { - 2} & { - 1} \cr 2 & 3 & 1 \cr 0 & 5 & { - 2} \cr } } \right]$$and$$...
GATE EE 1999
Find the eigen values and eigen vectors of the matrix $$\left[ {\matrix{ 3 & { - 1} \cr { - 1} & 3 \cr } } \... GATE EE 1999 If the vector$$\left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right]$$is an eigen vector of$$A = \left...
GATE EE 1998
$$A = \left[ {\matrix{ 2 & 0 & 0 & { - 1} \cr 0 & 1 & 0 & 0 \cr 0 & 0 & 3 & 0 \cr { - 1} & 0 & 0 & 4 ... GATE EE 1998 If$$A = \left[ {\matrix{ 5 & 0 & 2 \cr 0 & 3 & 0 \cr 2 & 0 & 1 \cr } } \right]$$then$${A^{ - 1}} = $... 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 Express the given matrix $$A = \left[ {\matrix{ 2 & 1 & 5 \cr 4 & 8 & {13} \cr 6 & {27} & {31} \cr } } ... GATE EE 1997 The inverse of the matrix$$S = \left[ {\matrix{ 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr 0 & 0 & 1 \cr } } \ri... GATE EE 1995 Given the matrix $$A = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 6} & { - 11} & { - 6} \cr } } \... GATE EE 1995 The rank of the following$$(n+1)x(n+1)$$matrix, where$$'a'$$is a real number is$$$\left[ {\matrix{ 1 ...
GATE EE 1995
$$A$$ $$\,\,5 \times 7$$ matrix has all its entries equal to $$1.$$ Then the rank of a matrix is
GATE EE 1994
The eigen values of the matrix $$\left[ {\matrix{ a & 1 \cr a & 1 \cr } } \right]$$ are
GATE EE 1994
The number of linearly independent solutions of the system of equations $$\left[ {\matrix{ 1 & 0 & 2 \cr 1 & { ... GATE EE 1994 ## Marks 2 More The eigen values of the matrix given below are$$\left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & { - 3} & ...
GATE EE 2017 Set 2
Let $$P = \left[ {\matrix{ 3 & 1 \cr 1 & 3 \cr } } \right].$$ Consider the set $$S$$ of all vectors $$\left(... GATE EE 2016 Set 2 Let the eigenvalues of a$$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} & 0 & { - 2} \cr 1 & { - 1} & 0 \cr...
GATE EE 2015 Set 1
$$A = \left[ {\matrix{ p & q \cr r & s \cr } } \right];B = \left[ {\matrix{ {{p^2} + {q^2}} & {pr + qs} ... GATE EE 2014 Set 3 A system matrix is given as follows$$$A = \left[ {\matrix{ 0 & 1 & { - 1} \cr { - 6} & { - 11} & 6 \cr { ... GATE EE 2014 Set 1 The equation $$\left[ {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr ... GATE EE 2013 A matrix has eigen values$$-1$$and$$-2.$$The corresponding eigenvectors are$$\left[ {\matrix{ 1 \cr { - 1} ... GATE EE 2013 The two vectors $$\left[ {\matrix{ 1 & 1 & 1 \cr } } \right]$$ and $$\left[ {\matrix{ 1 & a & {{a^2}} \cr ... GATE EE 2011 The matrix$$\left[ A \right] = \left[ {\matrix{ 2 & 1 \cr 4 & { - 1} \cr } } \right]$$is decomposed into a... GATE EE 2011 For the set of equations$$${x_1} + 2{x_2} + {x_3} + 4{x_4} = 2,$3{x_1} + 6{x_2} + 3{x_3} + 12{x_4} = 6.$$The f... GATE EE 2010 If the rank of a$$5x6$$matrix$$Q$$is$$4$$then which one of the following statements is correct? GATE EE 2008 Let$$P$$be$$2x2$$real orthogonal matrix and$$\overline x $$is a real vector$${\left[ {\matrix{ {{x_1}} & {{x_2... GATE EE 2008 $${q_1},\,{q_2},{q_3},.......{q_m}$$ are $$n$$-dimensional vectors with $$m ... GATE EE 2007 If$$A = \left[ {\matrix{ { - 3} & 2 \cr { - 1} & 0 \cr } } \right]$$then$$A$$satisfies the relation GATE EE 2007 If$$A = \left[ {\matrix{ { - 3} & 2 \cr { - 1} & 0 \cr } } \right]\,$$then$${A^9}$$equals GATE EE 2007 Let$$x$$and$$y$$be two vectors in a$$3-$$dimensional space and$$ $$denote their dot product. Then the determina... GATE EE 2007 For the matrix$$P = \left[ {\matrix{ 3 & { - 2} & 2 \cr 0 & { - 2} & 1 \cr 0 & 0 & 1 \cr } } \right],$...
GATE EE 2005
If $$R = \left[ {\matrix{ 1 & 0 & { - 1} \cr 2 & 1 & { - 1} \cr 2 & 3 & 2 \cr } } \right]$$ then the t...
GATE EE 2005

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