Question

If the trace of a matrix A is 3 then find the trace of 5A.​

Answer 1

Given:

Trace of matrix A is 3.

To find trace of 5A?

The trace of matrix is sum of principal diagonal elements,

$A=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

$A(trace)=1+1+1$

$A=3$

If trace of A is x, then

trace of $n-A\\x-A$

Given value is trace of A is 3,

$A(trace)=3\\Then\\5A=5*3\\5A(trace)=15$

Hence, trace of 5A is 15.