1
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
2
GATE EE 2021
Numerical
+2
-0
Let $A$ be a $10 \times 10$ matrix such that $A^5$ is null matrix and let $I$ be the $10 \times 10$ identity matrix. The determinant of $A+I$ is $\_\_\_\_$ .
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3
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The eigen values of the matrix given below are $$\left[ {\matrix{
0 & 1 & 0 \cr
0 & 0 & 1 \cr
0 & { - 3} & { - 4} \cr
} } \right]$$
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
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