91. The matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
{\frac{3}{2}}&0&{\frac{1}{2}} \\
0&{ - 1}&0 \\
{\frac{1}{2}}&0&{\frac{3}{2}}
\end{array}} \right]\] has three distinct eigen values and one of its eigen vectors is \[\left[ {\begin{array}{*{20}{c}}
1 \\
0 \\
1
\end{array}} \right].\]
Which one of the following can be another eigen vector of A?
Which one of the following can be another eigen vector of A?
92. The determinant \[\left| {\begin{array}{*{20}{c}}
{1 + {\text{b}}}&{\text{b}}&1 \\
{\text{b}}&{1 + {\text{b}}}&1 \\
2&{2{\text{b}}}&1
\end{array}} \right|\] equals to
93. The solution of the system of equations x + y + z = 4, x - y + z = 0, 2x + y + z = 5 is
94. Which one of the following is an eigen vector of the matrix \[\left[ {\begin{array}{*{20}{c}}
5&0&0&0 \\
0&5&5&0 \\
0&0&2&1 \\
0&0&3&1
\end{array}} \right]?\]
95. The system of equation, given below, has
x + 2y + 4z = 2
4x + 3y + z = 5
3x + 2y + 3z = 1
x + 2y + 4z = 2
4x + 3y + z = 5
3x + 2y + 3z = 1
96. The characteristic equation of a (3 × 3) matrix P is defined as
a(λ) = |P - λ$$I$$| = λ3 + λ2 + 2λ + 1 = 0
If $$I$$ denotes identity matrix, then the inverse of matrix P will be
a(λ) = |P - λ$$I$$| = λ3 + λ2 + 2λ + 1 = 0
If $$I$$ denotes identity matrix, then the inverse of matrix P will be
97. For \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
1&{\tan \,{\text{x}}} \\
{ - \tan {\text{ x}}}&1
\end{array}} \right],\] the determinant of ATA-1 is
98. The value of the determinant \[\left| {\begin{array}{*{20}{c}}
1&3&2 \\
4&1&1 \\
2&1&3
\end{array}} \right|\] is
99. The value of x3 obtained by solving following system of linear equation is
x1 + 2x2 - 2x3 = 4
2x1 + x2 + x3 = -2
-x1 + x2 - x3 = 2
x1 + 2x2 - 2x3 = 4
2x1 + x2 + x3 = -2
-x1 + x2 - x3 = 2
100. For what values of α and β, the following simultaneous equations have an infinite number of solutions?
x + y + z = 5
x + 3y + 3z = 9
x + 2y + αz = β
x + y + z = 5
x + 3y + 3z = 9
x + 2y + αz = β
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