1
GATE EE 1995
+1
-0.3
The inverse of the matrix $$S = \left[ {\matrix{ 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right]$$ is
A
$$\left[ {\matrix{ 1 & 0 & 1 \cr 0 & 0 & 0 \cr 0 & 1 & 1 \cr } } \right]$$
B
$$\left[ {\matrix{ 0 & 1 & 1 \cr { - 1} & { - 1} & 1 \cr 1 & 0 & 1 \cr } } \right]$$
C
$$\left[ {\matrix{ 2 & 2 & { - 2} \cr { - 2} & 2 & { - 2} \cr 0 & 2 & 2 \cr } } \right]$$
D
$$\left[ {\matrix{ {{1 \over 2}} & {{1 \over 2}} & {{{ - 1} \over 2}} \cr {{{ - 1} \over 2}} & {{1 \over 2}} & {{{ - 1} \over 2}} \cr 0 & 0 & 1 \cr } } \right]$$
2
GATE EE 1995
Subjective
+1
-0
Given the matrix $$A = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 6} & { - 11} & { - 6} \cr } } \right].\,\,$$ Its eigen values are
3
GATE EE 1995
+1
-0.3
The rank of the following $$(n+1)$$ $$x$$ $$(n+1)$$ matrix, where $$'a'$$ is a real number is $$\left[ {\matrix{ 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr . & {} & {} & {} & {} & {} & {} \cr . & {} & {} & {} & {} & {} & {} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr } } \right]$$\$
A
$$1$$
B
$$2$$
C
$$n$$
D
depends on the value of a
4
GATE EE 1994
+1
-0.3
$$A$$ $$\,\,5 \times 7$$ matrix has all its entries equal to $$1.$$ Then the rank of a matrix is
A
$$7$$
B
$$5$$
C
$$1$$
D
Zero
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