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If A is a 2x2 matrix with eigenvalues 3 and 5, what is the trace of A?

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Question: If A is a 2x2 matrix with eigenvalues 3 and 5, what is the trace of A?

Options:

  1. 8
  2. 15
  3. 5
  4. 3

Correct Answer: 8

Solution: 

The trace of a matrix is the sum of its eigenvalues. Therefore, trace(A) = 3 + 5 = 8.

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?
  1. 8
  2. 15
  3. 5
  4. 3

Questions & Step-by-Step Solutions

If A is a 2x2 matrix with eigenvalues 3 and 5, what is the trace of A?
  • 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.
  • Eigenvalues and Trace – The trace of a matrix is the sum of its eigenvalues, which is a fundamental property in linear algebra.
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