Problem 33
The sum of the eigen values of \(\left[\begin{array}{rrr}1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & -1 & -1\end{array}\right]\) is \(\begin{array}{lll}\text { (i) }-2 & \text { (ii) } 3 & \text { (iii) } 6\end{array}\) \((i w) 7\)
Problem 34
The maximum value of the rank of a \(4 \times 5\) matrix is .w.w.
Problem 38
The eigen values of a triangular matrix are ...
Problem 39
If the product of two eigen values of the matrix \(\left[\begin{array}{rrr}6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3\end{array}\right]\) is 16 , then the third eigen value is
Problem 40
If \(\lambda_{2}, i=1,2, \ldots \ldots \ldots n\) are the eigen values of a square matrix \(A\), then the eigen values of \(A^{T}\) are
Problem 43
If \(A=\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 5 \\ 0 & 0 & 3\end{array}\right]\), then eigen values of \(A^{-1}\) are.
Problem 45
If \(A=\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]\), then eigen values of \(\mathrm{A}^{-1}\) are ........
Problem 46
Matrix \(\left[\begin{array}{cc}x & 2 \\ 1 & x-1\end{array}\right]\) is singular for \(x=\ldots \ldots\)
Problem 48
The sum and product of the eigen values of \(\left[\begin{array}{lll}2 & 2 & 1 \\\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right]\) are ......... and
Problem 49
If \(A=\left[\begin{array}{rr}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A^{3}=\ldots \ldots .\)
