1
GATE ECE 2017 Set 2
Numerical
+2
-0
The rank of the matrix $$\left[ {\matrix{ 1 & { - 1} & 0 & 0 & 0 \cr 0 & 0 & 1 & { - 1} & 0 \cr 0 & 1 & { - 1} & 0 & 0 \cr { - 1} & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 & 1 & { - 1} \cr } } \right]$$ is __________.
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2
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If the vectors $${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$ and $${e_3} = \left( { - 2,0,1} \right)$$ form an orthogonal basis of the three dimensional real space $${R^3},$$ then the vectors $$u = \left( {4,3, - 3} \right) \in {R^3}$$ can be expressed as
A
$$u = - {2 \over 5}{e_1} - 3{e_2} - {{11} \over 5}{e_3}$$
B
$$u = - {2 \over 5}{e_1} - 3{e_2} + {{11} \over 5}{e_3}$$
C
$$u = - {2 \over 5}{e_1} + 3{e_2} + {{11} \over 5}{e_3}$$
D
$$u = - {2 \over 5}{e_1} + 3{e_2} - {{11} \over 5}{e_3}$$
3
GATE ECE 2016 Set 2
Numerical
+2
-0
The matrix $$A = \left[ {\matrix{ a & 0 & 3 & 7 \cr 2 & 5 & 1 & 3 \cr 0 & 0 & 2 & 4 \cr 0 & 0 & 0 & b \cr } } \right]$$ has det
$$(A)=100$$ and trace $$(A)=14.$$ The value of $$\left| {a - b} \right|$$ is ___________.
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4
GATE ECE 2016 Set 1
Numerical
+2
-0
A sequence $$x\left[ n \right]$$ is specified as $$$\left[ {\matrix{ {x\left[ n \right]} \cr {x\left[ {n - 1} \right]} \cr } } \right] = {\left[ {\matrix{ 1 & 1 \cr 1 & 0 \cr } } \right]^n}\left[ {\matrix{ 1 \cr 0 \cr } } \right],\,\,for\,\,n \ge 2.$$$
The initial conditions are $$x\left[ 0 \right] = 1,\,\,x\left[ 1 \right] = 1$$ and $$x\left[ n \right] = 0$$ for $$n < 0.$$ The value of $$x\left[ {12} \right]$$ is __________.
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