Engineering Mat...

Consider a matrix \(M = \left[ {\begin{array}{*{20}{c}} 1&2\\ 2&4 \end{array}} \right]\) if one of the eigenvectors is \(\left[ {\begin{array}{*{20}{c}} { - 2}\\ 1 \end{array}} \right]\) then what is the other vector the given matrix M?

Consider a matrix X_n×n, the two eigenvalues of the matrix are 6 and 10 + √-1). If n is equal to three then what is the trace of X?

Let M be a real 4 × 4 matrix. Consider the following statements:

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Consider a matrix M = PQT where  \(P=(^{12}_{9}) ,\ Q=(^{6}_{19})\).Note that QT denotes the transpose of Q. What is the largest eigenvalue of M?

Which is not the eigenvector for the given matrix

\(\left[ {\begin{array}{*{20}{c}} 3&1&4\\ 0&2&6\\ 0&0&5 \end{array}} \right]\) ?

Let Matrix \(A = \;\left[ {\begin{array}{*{20}{c}} a&4\\ 2&d \end{array}} \right]\)and the equation of A is A² – 4A = 5I where I is an identity matrix find the value of |a – d| respectively.

The matrix \(\left( \begin{matrix} 2 & -4 \\ 4 & -2 \\\end{matrix} \right)\) has

Consider a matrix  \(M =\left[ {\begin{array}{*{20}{c}} 2&0&0&0&2\\ 0&2&2&2&0\\ 0&2&2&2&0\\ 0&2&2&2&0\\ 2&0&0&0&2 \end{array}} \right]\). What is the product of the non-zero eigenvalue of M?

If \(Q = \left[ {\begin{array}{*{20}{c}}3&2&4\\2&0&2\\4&2&3\end{array}} \right]\) and \(P = \left[ {\begin{array}{*{20}{c}}{{v_1}}&{{v_2}}&{{v_3}}\end{array}} \right]\) is the matrix where v₁, v₂ and v₃ are linearly independent eigenvectors of the matrix Q, then the sum of the absolute values of all the elements of the matrix \({P^{ - 1}}QP\) is

Let the characteristic equation of a 3 X 3 Matrix A be \({\lambda ^3} + a{\lambda ^2} + 47\lambda \; - \;60 = 0\) if one eigenvalue of A is 4 and a is an integer value, then what is the smallest eigenvalue of A?