## True or False Statements

#### Chapter 1 Matrices and Linear Systems of Equations

1. In a diagonal matrix some of the diagonal elements may be zero

**Ans:** T

2. The product of two nonzero matrices is always a nonzero matrix

**Ans:** F

3. The rank of a singular matrix is one less than its order

**Ans:** F

4. The sum of two nonsingular matrices is always nonsingular

**Ans:** F

5. The product of two matrices is singular if either of them is singular

**Ans:** T

6. The system *x* − *y* = 2, *x* + *y* = 0 has a unique solution

**Ans:** T

7. The system *x* + *y* = 2, 2*x* + 2*y* = 4 has an infinite set of solutions

**Ans:** T

8. The system *x* + 2*y* = 1, 3*x* + 2*y* = 4 has no solution

**Ans:** F

#### Chapter 2 Eigenvalues and Eigenvectors

9. A matrix and its inverse have the same eigenvalues if *A* is orthogonal ...