1
GATE ECE 2013
+1
-0.3
The minimum eigenvalue of the following matrix is $$\left[ {\matrix{ 3 & 5 & 2 \cr 5 & {12} & 7 \cr 2 & 7 & 5 \cr } } \right]$$
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
2
GATE ECE 2013
+1
-0.3
Let $$A$$ be an $$m\,\, \times \,\,n$$ matrix and $$B$$ an $$n\,\, \times \,\,m$$ matrix. It is given that determinant $$\left( {{{\rm I}_m} + AB} \right) =$$determinant $$\left( {{{\rm I}_n} + BA} \right),$$ where $${{{\rm I}_k}}$$ is the $$k \times k$$ identity matrix. Using the above property, the determinant of the matrix given below is $$\left[ {\matrix{ 2 & 1 & 1 & 1 \cr 1 & 2 & 1 & 1 \cr 1 & 1 & 2 & 1 \cr 1 & 1 & 1 & 2 \cr } } \right]$$
A
$$2$$
B
$$5$$
C
$$8$$
D
$$16$$
3
GATE ECE 2012
+1
-0.3
Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the value of $${A^3}$$ is
A
$$15A+12$$ $${\rm I}$$
B
$$19A+30$$ $${\rm I}$$
C
$$17A+15$$ $${\rm I}$$
D
$$17A+21$$ $${\rm I}$$
4
GATE ECE 2011
+1
-0.3
The system of equations $$x+y+z=6,$$ $$x+4y+6z=20,$$ $$x + 4y + \lambda z = \mu$$ has no solution for values of $$\lambda$$ and $$\mu$$ given by
A
$$\lambda = 6,\,\,\mu = 20$$
B
$$\lambda = 6,\,\,\mu \ne 20$$
C
$$\lambda \ne 6,\,\,\mu = 20$$
D
$$\lambda \ne 6,\,\,\mu \ne 20$$
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