21. The rank of the matrix \[{\text{M}} = \left[ {\begin{array}{*{20}{c}}
5&{10}&{10} \\
1&0&2 \\
3&6&6
\end{array}} \right]\] is
22. One of the eigen vectors of the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
2&2 \\
1&3
\end{array}} \right]\] is
23. The lowest Eigen value of the 2 × 2 matrix \[\left[ {\begin{array}{*{20}{c}}
4&2 \\
1&3
\end{array}} \right]\]
24. Which one of the following statements is TRUE about every n × n matrix with only real eigen values?
25. The equation \[\left[ {\begin{array}{*{20}{c}}
2&{ - 2} \\
1&{ - 1}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{{{\text{x}}_1}} \\
{{{\text{x}}_2}}
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
0 \\
0
\end{array}} \right]\] has
26. Consider the system of simultaneous equations
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
This system has
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
This system has
27. The system of equations
x + y + z = 6
x + 4y + 6z = 20
x + 4y + \[\lambda \]z = \[\mu \]
has NO solution for values of \[\lambda \] and \[\mu \] given by
x + y + z = 6
x + 4y + 6z = 20
x + 4y + \[\lambda \]z = \[\mu \]
has NO solution for values of \[\lambda \] and \[\mu \] given by
28. Let the eigen values of a 2 × 2 matrix A be 1, -2 with eigen vectors x1 and x2 respectively. Then the eigen values and eigen vectors of the matrix A2 - 3A + 4$$I$$ would, respectively, be
29. The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A1B1C1 is
30. If the entries in each column of a square matrix M add up to 1, then an eiqen value of M is
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