1
GATE CSE 1994
Fill in the Blanks
+1
-0
The inverse of the matrix $$\left[ {\matrix{ 1 & 0 & 1 \cr { - 1} & 1 & 1 \cr 0 & 1 & 0 \cr } } \right]$$ is
2
GATE CSE 1994
MCQ (Single Correct Answer)
+1
-0.3
The rank of the matrix $$\left[ {\matrix{ 0 & 0 & { - 3} \cr 9 & 3 & 5 \cr 3 & 1 & 1 \cr } } \right]$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
3
GATE CSE 1993
MCQ (More than One Correct Answer)
+1
-0.3
The eigen vector (s) of the matrix
$$\left[ {\matrix{ 0 & 0 & \alpha \cr 0 & 0 & 0 \cr 0 & 0 & 0 \cr } } \right],\alpha \ne 0$$ is (are)
A
$$\left( {0,0,\alpha } \right)$$
B
$$\left( {\alpha ,0,0} \right)$$
C
$$\left( {0,0,1} \right)$$
D
$$\left( {0,\alpha ,0} \right)$$
4
GATE CSE 1993
Numerical
+1
-0
If $$A = \left[ {\matrix{ 1 & 0 & 0 & 1 \cr 0 & { - 1} & 0 & { - 1} \cr 0 & 0 & i & i \cr 0 & 0 & 0 & { - i} \cr } } \right]$$ the matrix $${A^4},$$
calculated by the use of Cayley - Hamilton theoram (or) otherwise is
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