Engineering Board Exam Reviewer · Eigenvalues and Eigenvectors · medium

An eigenvector of bmatrix4&1\2&3 bmatrix corresponding to =5 is

  1. bmatrix1\-2 bmatrix
  2. bmatrix1\-1 bmatrix
  3. bmatrix2\1 bmatrix
  4. bmatrix1\1 bmatrix

Answer

D. bmatrix1\1 bmatrix

Solution

(A-5I)v= bmatrix-1&1\2&-2 bmatrixv=0 -v1+v2=0 v1=v2. So v= bmatrix1\1 bmatrix (and its multiples). The vector bmatrix1\-2 bmatrix belongs to =2.

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  5. Find the trace of A5 if A= bmatrix1&2\2&1 bmatrix.
  6. A matrix A has eigenvalues 2 and 3. Find the eigenvalues of A2-3A+I.
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