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If A is a 2x2 matrix with eigenvalues 3 and 5, what is the trace of A?
Practice Questions
Q1
If A is a 2x2 matrix with eigenvalues 3 and 5, what is the trace of A?
8
15
5
3
Questions & Step-by-Step Solutions
If A is a 2x2 matrix with eigenvalues 3 and 5, what is the trace of A?
Steps
Concepts
Step 1: Understand what a 2x2 matrix is. A 2x2 matrix has 2 rows and 2 columns.
Step 2: Know that eigenvalues are special numbers associated with a matrix. In this case, the eigenvalues are given as 3 and 5.
Step 3: Learn that the trace of a matrix is defined as the sum of its eigenvalues.
Step 4: Add the eigenvalues together: 3 + 5.
Step 5: Calculate the sum: 3 + 5 = 8.
Step 6: Conclude that the trace of matrix A is 8.
No concepts available.
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