True/False Quiz for Chapter 3

Matrix Algebra

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1. A 2 x 3 matrix has two columns and three rows. True False

2. The transpose of a 2 x 3 matrix has two columns and three rows. True False

3. If A is a 2 x 3 matrix and B is a 3 x 2 matrix, then A+B is defined. True False

4. If A is a 2 x 3 matrix and B is a 3 x 2 matrix, then A-B is defined. True False

5. If A is a 2 x 3 matrix and B is a 3 x 2 matrix, then AB is defined. True False

6. If A is a 3 x 4 matrix and B is a 3 x 4 matrix, then A+B is defined. True False

7. If A is a 3 x 4 matrix and B is a 3 x 4 matrix, then A-B is defined. True False

8. If A is an invertible 3 x 4 matrix and B is a 3 x 4 matrix, then AB is defined. True False

9. It is never true that A+B, A-B, and AB are all defined. True False

10. If AB is defined, then BA must also be defined. True False

11. If AB and BA are both defined, they may have different dimensions. True False

12. If AB and BA are both defined and have the same dimensions, then they are equal. True False

13. If AX = B for any matrix A, then X = A^-1B. True False

14. If AX = B for a square matrix A, then X = A^-1B. True False

15. If AX = B for an invertible matrix A, then X = A^-1B. True False

16. The most efficient way to solve AX = B is to invert A. True False

17. Every matrix none of whose entries are zero is invertible. True False

18. Every invertible matrix is square and not equal to the zero matrix. True False

19. If one sector of the economy uses none of the products of another sector, then any increase in demand for the products of the first sector will have no effect on the second sector. True False

20. You can see the complete effect of one sector on another only by looking at the whole economy. True False