61. X = [x1, x2, ... xn]T is an n-tuple nonzero vector. The n × n matrix V = XXT
62. Which one of the following statements is NOT true for a square matrix A?
63. For any real, square and non-singular matrix B, the detB-1 is
64. Given a system of equations:
x + 2y + 2z = b1
5x + y + 3z = b2
Which of the following is true regarding its solution?
x + 2y + 2z = b1
5x + y + 3z = b2
Which of the following is true regarding its solution?
65. The matrix \[\left( {\begin{array}{*{20}{c}}
2&{ - 4} \\
4&{ - 2}
\end{array}} \right)\] has
66. The inverse of the matrix \[\left[ {\begin{array}{*{20}{c}}
2&3&4 \\
4&3&1 \\
1&2&4
\end{array}} \right]\] is
67. The condition for which the eigen values of the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
2&1 \\
1&{\text{k}}
\end{array}} \right]\] are positive, is
68. Given that the determinant of the matrix \[\left[ {\begin{array}{*{20}{c}}
1&3&0 \\
2&6&4 \\
{ - 1}&0&2
\end{array}} \right]\] is -12, the determinant of the matrix \[\left[ {\begin{array}{*{20}{c}}
2&6&0 \\
4&{12}&8 \\
{ - 2}&0&4
\end{array}} \right]\] is
69. For the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
5&3 \\
1&3
\end{array}} \right],\] ONE of the normalized eigen vectors is given as
70. The product of eigen values of the matrix P is \[{\text{P}} = \left[ {\begin{array}{*{20}{c}}
2&0&1 \\
4&{ - 3}&3 \\
0&2&{ - 1}
\end{array}} \right]\]
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