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If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?
If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?
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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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The trace of a matrix is the sum of its eigenvalues. Thus, trace(A) = 2 + 3 + 4 = 9.
Questions & Step-by-step Solutions
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Q
Q: If A is a 3x3 matrix with eigenvalues 2, 3, and 4, what is the trace of A?
Solution:
The trace of a matrix is the sum of its eigenvalues. Thus, trace(A) = 2 + 3 + 4 = 9.
Steps: 6
Show Steps
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.
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