The augmented matrix {1 -3 0 l 4}
0 1 2 l -1} represents a system with
a. one unique solution
b. two unique solutions
c. infinitely many solutions
d. no solution
e. none of the others
For the system described in the above matrix, which of the following is a solution to the system?
a. (-5, -2, -2)
b. (-11, -5, 2)
c. (0,0,3)
d. (3,-2,4)
e. noe of these are solutions
2007-01-22 14:49:25 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
2 equations in 3 unknowns has an infinite number of solutions.
One of the answers is right.
To start you out,
-5*1 -2(-2) + 0 ≠ 4
2007-01-22 15:05:06 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋
First, row reduce your augmented matrix.
[1 -3 0 | 4]
[0 1 2 | -1]
*
RREF
*
[1 0 6 | 1]
[0 1 2 | -1]
The solution to your system of equations is now
x1 = 1-6x3
x2 = -1-2x3
x3 = all real numbers
This leads you to conclude that the system has infinitely many solutions. As for the second part of your questions, try plugging the "solutions" into the equations we just found. One of them does work.
2007-01-23 05:29:13 · answer #2 · answered by Crystal 3 · 0⤊ 0⤋
sorry can't help you
i suggest rewriting the matrix...looked kinda confuzing
2007-01-22 22:53:27 · answer #3 · answered by Anonymous · 0⤊ 0⤋