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If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?

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Question: If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?

Options:

  1. 9
  2. 24
  3. 6
  4. 12

Correct Answer: 9

Solution: 

The trace of a matrix is the sum of its eigenvalues. Thus, trace(A) = 2 + 3 + 4 = 9.

If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?

Practice Questions

Q1
If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?
  1. 9
  2. 24
  3. 6
  4. 12

Questions & Step-by-Step Solutions

If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?
  • Step 1: Understand that a 3x3 matrix A has three eigenvalues.
  • Step 2: Identify the given eigenvalues of matrix A, which are 2, 3, and 4.
  • Step 3: Recall that the trace of a matrix is calculated by adding all of its eigenvalues together.
  • Step 4: Add the eigenvalues: 2 + 3 + 4.
  • Step 5: Calculate the sum: 2 + 3 = 5, then 5 + 4 = 9.
  • Step 6: Conclude that the trace of matrix A is 9.
  • Trace of a Matrix – The trace of a matrix is defined as the sum of its diagonal elements, which is also equal to the sum of its eigenvalues.
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