If \(A=\begin{bmatrix} -1 & 4 \\\ 5 & 8 \end{bmatrix}\), then trace of matrix A is

Question

Question

Answer 1

Concept:

Trace of a matrix:

Trace of a matrix is the sum of elements on the main diagonal.

The trace is only defined for a square matrix (n × n).

Let A be n × n matrix.

\(\rm tr\left( A \right) = \mathop \sum \limits_{n = 1}^n {A_{nn}}\)

Calculation:

Given: \(A=\begin{bmatrix} -1 & 4 \\\ 5 & 8 \end{bmatrix}\)

Trace of matrix = sum of elements on the main diagonal

= -1 + 8

= 7