Engineering Mathematics
Q61.
Let A be nxn real valued square symmetric matrix of rank 2 with \sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij}=50. Consider the following statements. (I) One eigen value must be in [-5, 5] (II) The eigen value with the largest magnitude must be strictly greater than 5. Which of the above statements about eigen values of A is/are necessarily CORRECT?Q62.
Consider a quadratic equation x^{2} -13x +36 = 0 with coefficients in a base b. The solutions of this equation in the same base b are x = 5 and x = 6. Then b = ___________.Q63.
Consider the systems,each consisting of m linear equations in n variables. I. If m \lt n, then all such systems have a solution II. If m \gt n, then none of these systems has a solution III. If m = n, then there exists a system which has a solution Which one of the following is CORRECT?Q64.
Suppose that the eigen values of matrix A are 1, 2, 4. The determinant of (A^{-1})^{T} is _________.Q65.
In the given matrix \begin{bmatrix} 1 & -1&2 \\ 0& 1 & 0\\ 1&2 & 1 \end{bmatrix}, one of the eigenvalues is 1. The eigenvectors corresponding to the eigenvalue 1 areQ66.
The larger of the two eigenvalues of the matrix \begin{bmatrix} 4 & 5\\ 2&1 \end{bmatrix} is _______.Q67.
Two eigen values of a 3x3 real matrix P are (2+\sqrt{-1}) and 3.The determinantof P is __________.Q68.
If the following system has non-trivial solution, px+qy+rz=0 qx+ry+pz=0 rx+py+qz=0, then which one of the following options is TRUE?Q70.
Consider the following 2x2 matrix A where two elements are unknown and are marked by a and b. The eigenvalues of this matrix are -1 and 7. What are the values of a and b? A=\begin{pmatrix} 1 & 4\\ b&a \end{pmatrix}.