Question

Find the trace of \left[\begin{array}{ccc}1&3&-5\\2&-1&5\\2&0&1\end{array}\right].

Answer 1

Trace of a Matrix

The Trace of a Square Matrix is defined as the sum of elements of its main diagonal.

Trace is defined only for a square matrix. The main diagonal refers to the diagonal running from the top-left to the bottom-right.

The trace of a square matrix A is denoted as tr(A).

Here our matrix, let us name it A, is:

$\sf A=\left[\begin{array}{ccc}\bold{1}&3&-5\\2&\bold{-1}&5\\2&0&\bold{1}\end{array}\right]$

As seen, the main diagonal elements are 1, -1 and 1.

So, trace is:

$\sf tr(A) = 1+(-1)+1 \\\\\\ \implies \huge \boxed{\sf tr(A)=1}$

Thus, the Trace is 1.