1
GATE EE 2022
+1
-0.33

Consider a 3 $$\times$$ 3 matrix A whose (i, j)-th element, ai,j = (i $$-$$ j)3. Then the matrix A will be

A
symmetric
B
skew-symmetric
C
unitary
D
null
2
GATE EE 2022
+1
-0.33

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.
3
GATE EE 2022
+1
-0.33

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
4
GATE EE 2017 Set 1
+1
-0.3
The matrix $$A = \left[ {\matrix{ {{3 \over 2}} & 0 & {{1 \over 2}} \cr 0 & { - 1} & 0 \cr {{1 \over 2}} & 0 & {{3 \over 2}} \cr } } \right]$$ has three distinct eigen values and one of its eigen vectors is $$\left[ {\matrix{ 1 \cr 0 \cr 1 \cr } } \right].$$ Which one of the following can be another eigen vector of $$A$$?
A
$$\left[ {\matrix{ 0 \cr 0 \cr { - 1} \cr } } \right]$$
B
$$\left[ {\matrix{ { - 1} \cr 0 \cr 0 \cr } } \right]$$
C
$$\left[ {\matrix{ 1 \cr 0 \cr { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ 1 \cr { - 1} \cr 1 \cr } } \right]$$
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