Match the Following

Chapter 1 Eigenvalues and Eigenvectors

  1. λi are eigenvalues of A and |A| 0
  2. One of the eigenvalues of A is zero
  3. λi are eigenvalues of A and λi 0 for all i
  4. λi are eigenvalues of orthogonal matrix A
  5. A, B, P are n-square matrices |P| ≠ 0 and B=P1AP
  6. D = [dij]is an n-square matrix with dij = 0 for ij
  7. Characteristic polynomials of A and A2are same
  8. Characteristic equation of A is λm = 0
  9. A is orthogonal
  1. A is singular
  2. 1 / λi are also eigenvalues of A
  3. A and B are similar
  4. |A | / λi are eigenvalues of Adj A
  5. A is nonsingular
  6. Characteristic polynomials of A and B are same
  7. dii are eigenvalues of D
  8. Characteristic equation of A is a reciprocal equation
  9. A is idempotent
  10. A is nilpotent with index m

Ans:

  1. d;
  2. a;
  3. e;
  4. b;
  5. c;
  6. g;
  7. i;

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