81
How many solutions does the following system of linear equations have?
A)
infinitely many
B)
two distinct solutions
C)
unique
D)
none
Answer & Solution
Answer: Option
C
82
Consider the following matrix.
A)
x = 4, y = 10
B)
x = 5, y = 8
C)
x = -3, y = 9
D)
x = -4, y = 10
Answer & Solution
Answer: Option
D
83
Let N be a 3 by 3 matrix with real number entries. The matrix N is such that N2 = 0. The eigen values of N are
A)
0, 0, 0
B)
0, 0, 1
C)
0, 1, 1
D)
1, 1, 1
Answer & Solution
Answer: Option
A
84
The eigen values of a (2 × 2) matrix X are -2 and -3. The eigen values of the matrix (X + $$I$$) (X + 5$$I$$) are
A)
-3, -4
B)
-1, -2
C)
-1, -3
D)
-2, -4
Answer & Solution
Answer: Option
A
85
If the following system has non-trivial solution,
A)
p - q + r = 0 or p = q = -r
B)
p + q - r = 0 or p = -q = r
C)
p + q + r = 0 or p = q = r
D)
p - q + r = 0 or p = -q = -r
Answer & Solution
Answer: Option
C
86
The sum of the eigen values of the matrix given below is \[\left[ {\begin{array}{*{20}{c}}
1&2&3 \\
1&5&1 \\
3&1&1
\end{array}} \right].\]
A)
5
B)
7
C)
9
D)
18
Answer & Solution
Answer: Option
B
87
The following system of equations1 + x2 + 2x3 = 11 + 2x3 + 3x3 = 21 + 4x2 + ax3 = 4
A)
0
B)
either 0 or 1
C)
one of 0, 1 or -1
D)
any real number other than 5
Answer & Solution
Answer: Option
D
88
The eigen vector pair of the matrix \[\left[ {\begin{array}{*{20}{c}}
3&4 \\
4&{ - 3}
\end{array}} \right]\] is
A)
\[\left[ {\begin{array}{*{20}{c}}
1 \\
2
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1 \\
{ - 2}
\end{array}} \right]\]
B)
\[\left[ {\begin{array}{*{20}{c}}
2 \\
1
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1 \\
{ - 2}
\end{array}} \right]\]
C)
\[\left[ {\begin{array}{*{20}{c}}
2 \\
{ - 1}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1 \\
{ - 2}
\end{array}} \right]\]
D)
\[\left[ {\begin{array}{*{20}{c}}
{ - 2} \\
1
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1 \\
2
\end{array}} \right]\]
Answer & Solution
Answer: Option
B
89
For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?
A)
(MT )T = M
B)
(cM)T = c(M)T
C)
(M + N)T = MT + NT
D)
MN = NM
Answer & Solution
Answer: Option
D
90
The following vector is linearly dependent upon the solution to the previous problem
A)
\[\left[ {\begin{array}{*{20}{c}}
8 \\
9 \\
3
\end{array}} \right]\]
B)
\[\left[ {\begin{array}{*{20}{c}}
{ - 2} \\
{ - 17} \\
{30}
\end{array}} \right]\]
C)
\[\left[ {\begin{array}{*{20}{c}}
4 \\
4 \\
5
\end{array}} \right]\]
D)
\[\left[ {\begin{array}{*{20}{c}}
{13} \\
2 \\
{ - 3}
\end{array}} \right]\]
Answer & Solution
Answer: Option
B
