71
The minimum eigen value of the following matrix is
A)
0
B)
1
C)
2
D)
3
Answer & Solution
Answer: Option
A
72
With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates; (x1 , y1 ) = (1, 0);
(x2 , y2 ) = (2, 2); (x3 , y3 ) = (4, 3). The area of the triangle is equal to
A)
\[\frac{3}{2}\]
B)
\[\frac{3}{4}\]
C)
\[\frac{4}{5}\]
D)
\[\frac{5}{2}\]
Answer & Solution
Answer: Option
A
73
If a square matrix A is real and symmetric, then the eigen values
A)
are always real
B)
are always real and positive
C)
are always real and non-negative
D)
occur in complex conjugate pairs
Answer & Solution
Answer: Option
A
74
An eigen vector of \[{\text{P}} = \left[ {\begin{array}{*{20}{c}}
1&1&0 \\
0&2&2 \\
0&0&3
\end{array}} \right]\] is
A)
[-1 1 1]T
B)
[1 2 1]T
C)
[1 -1 2]T
D)
[2 1 -1]T
Answer & Solution
Answer: Option
B
75
Given the matrix \[\left[ {\begin{array}{*{20}{c}}
{ - 4}&2 \\
4&3
\end{array}} \right],\] the eigen vector is
A)
\[\left[ {\begin{array}{*{20}{c}}
3 \\
2
\end{array}} \right]\]
B)
\[\left[ {\begin{array}{*{20}{c}}
4 \\
3
\end{array}} \right]\]
C)
\[\left[ {\begin{array}{*{20}{c}}
2 \\
{ - 1}
\end{array}} \right]\]
D)
\[\left[ {\begin{array}{*{20}{c}}
{ - 1} \\
2
\end{array}} \right]\]
Answer & Solution
Answer: Option
C
76
At least one eigen value of a singular matrix is
A)
positive
B)
zero
C)
negative
D)
imaginary
Answer & Solution
Answer: Option
B
77
Eigen values of a real symmetric matrix are always
A)
positive
B)
negative
C)
real
D)
complex
Answer & Solution
Answer: Option
C
78
The eigen values of a skew-symmetric matrix are
A)
always zero
B)
always pure imaginary
C)
either zero or pure imaginary
D)
always real
Answer & Solution
Answer: Option
C
79
Which one of the following does NOT equal \[\left| {\begin{array}{*{20}{c}}
1&{\text{x}}&{{{\text{x}}^2}} \\
1&{\text{y}}&{{{\text{y}}^2}} \\
1&{\text{z}}&{{{\text{z}}^2}}
\end{array}} \right|?\]
A)
\[\left| {\begin{array}{*{20}{c}}
1&{{\text{x}}\left( {{\text{x}} + 1} \right)}&{{\text{x}} + 1} \\
1&{{\text{y}}\left( {{\text{y}} + 1} \right)}&{{\text{y}} + 1} \\
1&{{\text{z}}\left( {{\text{z}} + 1} \right)}&{{\text{z}} + 1}
\end{array}} \right|\]
B)
\[\left| {\begin{array}{*{20}{c}}
1&{{\text{x}} + 1}&{{{\text{x}}^2} + 1} \\
1&{{\text{y}} + 1}&{{{\text{y}}^2} + 1} \\
1&{{\text{z}} + 1}&{{{\text{z}}^2} + 1}
\end{array}} \right|\]
C)
\[\left| {\begin{array}{*{20}{c}}
0&{{\text{x}} - {\text{y}}}&{{{\text{x}}^2} - {{\text{y}}^2}} \\
0&{{\text{y}} - {\text{z}}}&{{{\text{y}}^2} - {{\text{z}}^2}} \\
1&{\text{z}}&{{{\text{z}}^2}}
\end{array}} \right|\]
D)
\[\left| {\begin{array}{*{20}{c}}
2&{{\text{x}} + {\text{y}}}&{{{\text{x}}^2} + {{\text{y}}^2}} \\
2&{{\text{y}} + {\text{z}}}&{{{\text{y}}^2} + {{\text{z}}^2}} \\
1&{\text{z}}&{{{\text{z}}^2}}
\end{array}} \right|\]
Answer & Solution
Answer: Option
A
80
The inverse of the 2 × 2 matrix \[\left[ {\begin{array}{*{20}{c}}
1&2 \\
5&7
\end{array}} \right]\] is
A)
\[\frac{1}{3}\left[ {\begin{array}{*{20}{c}}
{ - 7}&2 \\
5&{ - 1}
\end{array}} \right]\]
B)
\[\frac{1}{3}\left[ {\begin{array}{*{20}{c}}
7&2 \\
5&1
\end{array}} \right]\]
C)
\[\frac{1}{3}\left[ {\begin{array}{*{20}{c}}
7&{ - 2} \\
{ - 5}&1
\end{array}} \right]\]
D)
\[\frac{1}{3}\left[ {\begin{array}{*{20}{c}}
{ - 7}&{ - 2} \\
{ - 5}&{ - 1}
\end{array}} \right]\]
Answer & Solution
Answer: Option
A
