1
GATE CE 1999
+1
-0.3
The equation $$\left[ {\matrix{ 2 & 1 & 1 \cr 1 & 1 & { - 1} \cr y & {{x^2}} & x \cr } } \right] = 0$$ represents a parabola passing through the points.
A
$$(0, 1), (0, 2), (0, -1)$$
B
$$(0, 0), (-1, 1), (1, 2)$$
C
$$(1, 1), (0, 0), (2, 2)$$
D
$$(1, 2), (2, 1), (0, 0)$$
2
GATE CE 1998
+1
-0.3
In matrix algebra $$AS=AT$$ ($$A,S,T,$$ are matrices of appropriate order) implies $$S=T$$ only if
A
$$A$$ is symmetric
B
$$A$$ is singular
C
$$A$$ is non singular
D
$$A$$ is skew - symmetric
3
GATE CE 1998
+1
-0.3
If $$A$$ is a real square matrix then $$A{A^T}$$ is
A
un symmetric
B
always symmetric
C
skew - symmetric
D
some times symmetric
4
GATE CE 1998
+1
-0.3
The real symmetric matrix $$C$$ corresponding to the quadratic form $$Q = 4{x_1}{x_2} - 5{x_2}{x_2}$$ is
A
$$\left[ {\matrix{ 1 & 2 \cr 2 & { - 5} \cr } } \right]$$
B
$$\left[ {\matrix{ 2 & 0 \cr 0 & { - 5} \cr } } \right]$$
C
$$\left[ {\matrix{ 1 & 1 \cr 1 & { - 2} \cr } } \right]$$
D
$$\left[ {\matrix{ 0 & 2 \cr 2 & { - 5} \cr } } \right]$$
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