Dr. Mark V. Sapir
Homework due Class 2.
1. Find the solution set of each of the following linear equations.
Homework due Class 3.
1. The curve y = ax2 + bx + c shown in the figure passes through the points (x1,y1), (x2,y2), and (x3,y3). Show that the coefficients, a, b, c are a solution of the system of linear equations whose augmented matrix is
|[ x12||x1||1||y1 ]|
|[ x22||x2||1||y2 ]|
|[ x32||x3||1||y3 ]|
Homework due Class 4.
1. The figure below shows the graph of a cubic equation y = ax3 + bx2 + cx + d. Find the coefficients a, b, c and d.
Homework due Class 5.
1. Solve each of the following systems by Gauss-Jordan elimination.
3x1 + 2x2 - x3 = -15 5x1 + 3x2 + 2x3 = 0 3x1 + x2 + 3x3 = 11 -6x1 - 4x2 + 2x3 = 30 10y - 4z + w = 1 x + 4y - z + w = 2 3x + 2y + z + 2w = 5 -2x - 8y + 2z - 2w = -4 x - 6y + 3z = 1
x + 2y - 3z = 4 3x - y + 5z = 2 4x + y + (a2-14)z = a+2