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Elementary and Intermediate Algebra
Mark Dugopolski, Southeastern Louisiana University

Systems of Linear Equations and Inequalities
Solving Linear Systems Using Matrices

Warm-Ups



1

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The augmented matrix for x + 3y = 5 and -x - 3y = 2 is matrix (a).
A)TRUE
B)FALSE
2

The augmented matrix for 2y - x = -3 and 2x - 4y = 3 is matrix (c).
A)TRUE
B)FALSE
3

Matrix (a) is equivalent to matrix (b).
A)TRUE
B)FALSE
4

Matrix (c) is equivalent to matrix (d).
A)TRUE
B)FALSE
5

The system corresponding to matrix (b) is inconsistent.
A)TRUE
B)FALSE
6

The system corresponding to matrix (c) is dependent.
A)TRUE
B)FALSE
7

The system corresponding to matrix (d) is independent.
A)TRUE
B)FALSE
8

The augmented matrix for a system of two linear equations and two unknowns is a 2 x 2 matrix.
A)TRUE
B)FALSE
9

The notation 2R1 + R3 → R3 means to replace R3 by 2R1 + R3.
A)TRUE
B)FALSE
10

The notation R1 ↔ R2 means to replace R2 by R1.
A)TRUE
B)FALSE