Engineering Board Exam Reviewer · Eigenvalues and Eigenvectors · medium

Find the largest eigenvalue of bmatrix2&0&0\0&3&4\0&4&9 bmatrix.

  1. 9
  2. 11
  3. 12
  4. 3

Answer

B. 11

Solution

The matrix is block diagonal. =2 comes from the 1×1 block. For bmatrix3&4\4&9 bmatrix: (3- )(9- )-16= 2-12 +11=0 =1,11. The largest eigenvalue is 11.

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