Question

1.) Find the values of a, b, and c that will make the statement true.
[5 a -2] [5 102]
[3 4 –b] = [-3 -4 3]
[2c 5 9] [-2 5 9]
a.) 8R1-R2--> =R2
b.) -8R1-R2 -> =R2
c.) –8R1 +R2 -> =R2
d.) 8R1-R2 -> =R2

2.) Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter.
-x+y+z=0
3x+2y+5z=18
15x+10y+25z=89
A.) (3,2,1)
B.) (3,2,0)
C.) Coincident dependence; {(x,y,z) |-x+y-z=0
D.) No solution, inconsistent

3.) Solve the system by triangularizing the augmented matrix and using back substitution. If the system is linearly dependent, give the solution in terms of a parameter.

X+y-z=3
x-y-2z=6
2x-y+z=3

A.) (0,0,-4)
B.) (0,0,-3)
C.) Coincident dependence; {(x,y,z) | -x+y-z=3
D.) No solution, inconsistent