List of top Engineering Mathematics Questions on Linear Algebra

What is the 2's complement representation of the decimal number -5 in 8-bit binary?

Which of the following circuits is a sequential circuit?

Let the matrix \[ A=\begin{bmatrix} 3& 1 -1& 2 \end{bmatrix} \] and \[ I=\begin{bmatrix} 1& 0 0& 1 \end{bmatrix}, \] then \[ A^{2}-5A+7I= \]

Let \(A\) and \(B\) be any two \(n\times n\) matrices and \[ tr(A)=\sum_{i=1}^{n}a_{ii}, \qquad tr(B)=\sum_{i=1}^{n}b_{ii}. \] Consider the following statements: \begin{itemize
• Statement-I : \(tr(AB)=tr(BA)\).
• Statement-II : \(tr(A+B)=tr(A)+tr(B)\).
• Statement-III : If \(tr(A)=5,\; tr(A^{2})=13\), then \[ tr(A-I)^2=6, \] where \(A_{3\times3}\) and \(I_{3\times3}\) are matrices. Choose the correct option. }

Let the matrix \[ A=\begin{bmatrix} 3& 1 \\ -1& 2 \end{bmatrix} \] and \[ I=\begin{bmatrix} 1& 0 \\ 0& 1 \end{bmatrix}, \] then \[ A^{2}-5A+7I= \]

Let \(A\) and \(B\) be any two \(n\times n\) matrices and \[ tr(A)=\sum_{i=1}^{n}a_{ii}, \qquad tr(B)=\sum_{i=1}^{n}b_{ii}. \] Consider the following statements:
• Statement-I : \(tr(AB)=tr(BA)\).
• Statement-II : \(tr(A+B)=tr(A)+tr(B)\).
• Statement-III : If \(tr(A)=5,\; tr(A^{2})=13\), then \[ tr(A-I)^2=6, \] where \(A_{3\times3}\) and \(I_{3\times3}\) are matrices. Choose the correct option.

The Eigenvalues of \(3\times 3\) real matrix A are 1, 2, 3 then \(A^{-1} =\)