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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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