Question

define a trace of a matrix and find the trace of A if A=[1 2 -1/2 0 -1 2-1/2 2 1]​

Answer 1

SOLUTION

TO DETERMINE

1. Define trace of a matrix

2. The trace of A where

$\displaystyle A = \begin{pmatrix} 1 & 2 & - \frac{1}{2} \ \\ \\ \ 0 & - 1 & 2 \\ \\ - \frac{1}{2} & 2 & 1 \end{pmatrix}$

EVALUATION

1. For any square matrix A the trace of A is denoted by trace A and defined as sum of elements on the main diagonal of A.

2. Here the given matrix is

$\displaystyle A = \begin{pmatrix} 1 & 2 & - \frac{1}{2} \ \\ \\ \ 0 & - 1 & 2 \\ \\ - \frac{1}{2} & 2 & 1 \end{pmatrix}$

Now the elements on the main diagonal of A are 1 , - 1 , 1

Hence the required trace A

= Sum of elements on the main diagonal of A

= 1 - 1 + 1

= 1

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