1
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
2
GATE EE 1994
+1
-0.3
The eigen values of the matrix $$\left[ {\matrix{ a & 1 \cr a & 1 \cr } } \right]$$ are
A
$$(a+1),0$$
B
$$a,0$$
C
$$(a-1),0$$
D
$$0,0$$
3
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
4
GATE EE 1994
+1
-0.3
The number of linearly independent solutions of the system of equations
$$\left[ {\matrix{ 1 & 0 & 2 \cr 1 & { - 1} & 0 \cr 2 & { - 2} & 0 \cr } } \right]\,\,\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right] = 0$$ is equal to
A
$$1$$
B
$$2$$
C
$$3$$
D
$$0$$
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