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Math 1314 Exam 4 Review A. Baumgardner 1. True or False: a. A system of equations represented by a represent of ii lines with the same slope always has no solution. b. A system of equations represented by a graph of two lines with slopes that are negative reciprocals always has one solution. c. If two lines do not have exactly one catamenia of intersection then they must be parallel. d. The system of equations Ax ? By = 1 and ? Ax + By = ?1 has no solution. e. A non-square matrix cannot have a erratic solution. f. The mathematical function for Gaussian elimination can be used plainly for square matrices. g. A square matrix that has a unique solution has a bring down matrix with 1s along the one-sided and 0s above and below the 1s. h. A square matrix with an all-zero form has infinitely many solutions.

2. Solve the give systems of linear equations by substitution. completely solutions must be scripted as consistent pairs. x + y = 3 a. x ? y = 1 b.
2x + y = 7 ?2 x ? y = 5 4x ? y = 1 8x ? 2 y = 2

c.

3. Solve the given systems of linear equations by elimination. All solutions must be written as ordered pairs. ?4 x + 2 y = 3 a. 4x ? y = 5 b.
2x + 5 y = 5 ?4 x ? 10 y = ?10 2x + 5 y = 5 ?4 x ? 10 y = 10

c.

4. Solve the given systems of linear equation by graphing. All solutions must be written as ordered pairs. 5x + 2 y = 3 a. 4x ? 2 y = 6 b.
5x ? y = 2 5 x ? y = ?2 x + 2 y = ?6 2 x + 4 y = ?12

c.

5.



What is the size (order) of the following matrices? ? 5? a. ? ?7 ? ? ? ? 9? ? ?
? 9 ?5 3 2 7 ? b. ? ?1 2 0 ?2 ?3? ? ? ? 1 3 ?5 7 9 ? ? ?

6. Solve for the indicated variables. ? 2a ? 1 3 4c + 2 ? ?9 5 ? 2b 2 ? a. ? d 2 2d 11 ? ?6 7e + 2 ? = ?9 ? ? ? ? ?4 g ? 9 h 72 ? ?5 17 72 ? ? ? ? ?
1? ? 9 ? ?4 x ? ? ?w +1 b. ? 2 ?= ? ? y ? 3 z + 7? ?3 3 ? ?

7. State whether or not apiece matrix is in row-echelon form (REF). If it is, determine whether it is in reduced row-echelon form (RREF). State your answer using complete sentences. 4? ?1 0 0 ?0 1 1 2? a. ? ? ? 0 0 1 ?7 ? ? ?
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