1
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

e4 denotes the exponential of a square matrix A. Suppose $$\lambda$$ is an eigen value and v is the corresponding eigen-vector of matrix A.

Consider the following two statements:

Statement 1 : e$$\lambda$$ is an eigen value of eA.

Statement 2 : v is an eigen-vector of eA.

Which one of the following options is correct?

A
Statement 1 is true and statement 2 is false.
B
Statement 1 is false and statement 2 is true.
C
Both the statements are correct.
D
Both the statements are false.
2
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Consider a matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 2} \cr 0 & 1 & 1 \cr } } \right]$$. The matrix A satisfies the equation 6A$$-$$1 = A2 + cA + dI, where c and d are scalars and I is the identify matrix. Then (c + d) is equal to

A
5
B
17
C
$$-$$6
D
11
3
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The eigen values of the matrix given below are $$\left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & { - 3} & { - 4} \cr } } \right]$$
A
$$(0,-1,-3)$$
B
$$(0,-2,-3)$$
C
$$(0,2,3)$$
D
$$(0,1,3)$$
4
GATE EE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let $$P = \left[ {\matrix{ 3 & 1 \cr 1 & 3 \cr } } \right].$$ Consider the set $$S$$ of all vectors $$\left( {\matrix{ x \cr y \cr } } \right)$$ such that $${a^2} + {b^2} = 1$$ where $$\left( {\matrix{ a \cr b \cr } } \right) = P\left( {\matrix{ x \cr y \cr } } \right).$$ Then $$S$$ is
A
a circle of radius $$\sqrt {10} $$
B
a circle of radius $${1 \over {\sqrt {10} }}$$
C
an ellipse with major axis along $$\left( {\matrix{ 1 \cr 1 \cr } } \right)$$
D
an ellipse with minor axis along $$\left( {\matrix{ 1 \cr 1 \cr } } \right)$$
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