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Engineering Mathematics, Volume 2 by E. Rukmangadachari

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True or Flase Statements

Chapter 1 Eigenvalues and Eigenvectors

  1. A matrix and its inverse have the same eigen values if A is orthogonal.

    Ans: T

  2. Two linearly independent eigenvectors may correspond to an eigenvalue λ of a matrix.

    Ans: T

  3. Cayley–Hamilton Theorem is applicable to every matrix.

    Ans: F

  4. A square matrix with repeated eigenvalues is not diagonalizable.

    Ans: F

  5. Powers of a square matrix can be found using diagonalization.

    Ans: T

  6. Every real square matrix can be uniquely expressed as the sum of a symmetric and a skew-symmetric matrix.

    Ans: T

  7. If A and B are symmetric then AB is symmetric.

    Ans: F

    Chapter 2 Quadratic Forms

  8. If A is a symmetric matrix with distinct eigenvalues then its eigenvectors are orthogonal.

    Ans: T

  9. A square matrix with two ...

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