Trace From Eigenvalues

Linear Algebra
Eigenvalues
Easy
A matrix has eigenvalues , , and . What is its trace?
Hint 1

The trace of a matrix equals the sum of its eigenvalues, counted with multiplicity.

Hint 2

Add the three given eigenvalues directly.

Show worked solution
  1. 1. Apply the trace-eigenvalue identity

    For any square matrix, the trace equals the sum of its eigenvalues.

  2. 2. Add

    Summing the eigenvalues gives the trace.

Answer: 11

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