In Problems 1-4, write the augmented matrix of the system of linear equations. (If necessary, review the terminology of Section 4.2.) 1. x1 +2x2 +3x3 =12 x1 +7x2 -5x3 =15

2. 4x1 + x2 =8 3x1 -5x2 =6 x1 +9x2 =4

Solve Problems 47-62 using Gauss-Jordan elimination

1.

2x1 - x2 -3x3 =8 x1 -2x2 =7

2.

3x1 -4x2 - x3 =1 2x1 -3x2 + x3 =1 x1 -2x2 +3x3 =2

3.

4x1 -2x2 +2x3 = 5 -6x1 +3x2 -3x3 =-2 10x1 -5x2 +9x3 = 4

Consider a consistent system of three linear equations in three variables. Discuss the nature of the system and its solution set if the reduced form of the augmented coefficient matrix has

(A) One leftmost 1 (B) Two leftmost 1's (C) Three leftmost 1's (D) Four leftmost 1's

Airplane leases. A corporation wants to lease a fleet of 12 airplanes with a combined carrying capacity of 220 pas-sengers. The three available types of planes carry 10, 15, and 20 passengers, respectively. How many of each type of plane should be leased?

Find a, b, and c so that the graph of the quadratic equation y =ax^2+bx +c passes through the points (-1,-5), (2,7), and (5,1)