Linear Algebra MCQs Question and Answer in Engineering Maths

The transformation matrix for mirroring a point in x-y plane about the line y = x is given by

For the matrix, \[\left[ {\begin{array}{*{20}{c}} 4&1 \\ 1&4 \end{array}} \right]\]  the eigen values are

For the matrix A satisfying the equation given below, the eigen values are
\[\left[ {\text{A}} \right]\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 7&8&9 \\ 4&5&6 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 4&5&6 \\ 7&8&9 \end{array}} \right]\]

The matrix \[{\text{M}} = \left[ {\begin{array}{*{20}{c}} { - 2}&2&{ - 3} \\ 2&1&{ - 6} \\ { - 1}&{ - 2}&0 \end{array}} \right]\]    has eigen values -3, -3, 5. An eigen vector corresponding to the eigen value 5 is [1 2 -1]^T. One of the eigen vectors of the matrix M³ is

The inverse of the matrix \[\left[ {\begin{array}{*{20}{c}} {3 + 2{\text{i}}}&{\text{i}} \\ { - {\text{i}}}&{3 - 2{\text{i}}} \end{array}} \right]\]   is

In matrix equation [A]{X} = {R}
\[\left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}} 4&8&4 \\ 8&{16}&{ - 4} \\ 4&{ - 4}&{15} \end{array}} \right],\,\left\{ {\text{X}} \right\} = \left\{ {\begin{array}{*{20}{c}} 2 \\ 1 \\ 4 \end{array}} \right\}\,{\text{and }}\left\{ {\text{R}} \right\} = \left\{ {\begin{array}{*{20}{c}} {32} \\ {16} \\ {64} \end{array}} \right\}\]
One of the eigen values of Matrix [A] is

Consider a 2 × 2 square matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} \sigma &{\text{x}} \\ \omega &\sigma \end{array}} \right]\]   where x is unknown. If the eigen values of the matrix A are \[\left( {\sigma + {\text{j}}\omega } \right)\]  and \[\left( {\sigma - {\text{j}}\omega } \right)\]  , then x is equal to

Solution for the system defined by the set of equations 4y + 3z = 8; 2x - z = 2 and 3x + 2y = 5 is

The solution to the system of equations is \[\left[ {\begin{array}{*{20}{c}} 2&5 \\ { - 4}&3 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\text{x}} \\ {\text{y}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 2 \\ { - 30} \end{array}} \right]\]

For the given orthogonal matrix Q
\[{\text{Q}} = \left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}} \\ { - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}} \\ {\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}} \end{array}} \right]\]
The inverse is