1
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 __________.
Your input ____
2
GATE ECE 2009
MCQ (Single Correct Answer)
+2
-0.6
The eigen values of the following matrix $$\left[ {\matrix{ { - 1} & 3 & 5 \cr { - 3} & { - 1} & 6 \cr 0 & 0 & 3 \cr } } \right]$$ are
A
$$3, 3 + 5j, 6 - j$$
B
$$-6 + 5j, 3 + j, 3 - j$$
C
$$3+j, 3-j, 5+j$$
D
$$3, -1+3j, -1-3j$$
3
GATE ECE 2006
MCQ (Single Correct Answer)
+2
-0.6
The eigen values and the correspondinng eigen vectors of a $$2 \times 2$$ matrix are given by

Eigen value
$${\lambda _1} = 8$$
$${\lambda _2} = 4$$

Eigen vector
$${V_1} = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$
$${V_2} = \left[ {\matrix{ 1 \cr -1 \cr } } \right]$$

The matrix is

A
$$\left[ {\matrix{ 6 & 2 \cr 2 & 6 \cr } } \right]$$
B
$$\left[ {\matrix{ 4 & 6 \cr 6 & 4 \cr } } \right]$$
C
$$\left[ {\matrix{ 2 & 4 \cr 4 & 2 \cr } } \right]$$
D
$$\left[ {\matrix{ 4 & 8 \cr 8 & 4 \cr } } \right]$$
4
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
Given an orthogonal matrix $$A = \left[ {\matrix{ 1 & 1 & 1 & 1 \cr 1 & 1 & { - 1} & { - 1} \cr 1 & { - 1} & 0 & 0 \cr 0 & 0 & 1 & { - 1} \cr } } \right]$$ then the value of $${\left( {A{A^T}} \right)^{ - 1}}$$ is
A
$${1 \over 4}{{\rm I}_4}$$
B
$${1 \over 2}{{\rm I}_4}$$
C
$${\rm I}$$
D
$${1 \over 3}{{\rm I}_4}$$
GATE ECE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12