What is the trace of matrix A?
Understand the Problem
The question asks to define the trace of a matrix and provides an example calculation. The trace is the sum of the elements on the main diagonal.
Answer
The trace of matrix $A$ is 21. $tr(A) = 21$
Answer for screen readers
The trace of matrix A is 21.
$tr(A) = 5 + 9 + 7 = 21$
Steps to Solve
- Identify the diagonal elements
The diagonal elements of matrix $A$ are 5, 9, and 7.
- Sum the diagonal elements
Add the diagonal elements together: $5 + 9 + 7 = 21$
The trace of matrix A is 21.
$tr(A) = 5 + 9 + 7 = 21$
More Information
The trace is only defined for square matrices (matrices with the same number of rows and columns). It's a useful concept in linear algebra and has connections to eigenvalues and matrix similarity.
Tips
A common mistake is to add off-diagonal elements instead of the elements on the main diagonal. Another mistake is to only add two of the three elements. Remember to include all the entries in the main diagonal.
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