Download 7.3 Worksheet Find the reduced row echelon form for the matrix. 1

7.3 Worksheet
Find the reduced row echelon form for the matrix.
2
1. [−1
0
0 1
3
1 0
2]
2 −3 −1
1
2. [3
2
0 2 1
2 4 7]
1 3 4
R2 + R1
-3R1 + R2
R1 + R2
-2R1 + R3
½ R2
½ R2
-R2 + R1
-2R2 + R3
-R2 + R3
-1/4R3
1
2
3
1
3. [
]
−3 −5 −7 −4
3R1 + R2
-1/2R3 + R1
-1/2R3 +R2
-2R2 + R1
Try on your own on the back.
1 −2
4. [ 3 −5
−2 4
3 −5
2
6
−3
6
1
1
3 −1]
−2 5
4 −3
Solve the system of equations by finding the reduced row echelon form of the matrix.
1. x + 2y – z = 3
3. x + y + 3z = 2
3x + 7y – 3z = 12
3x + 4y + 10z = 5
-2x – 4y + 3z = -5
x + 2y + 4z = 3
Augmented Matrix:
Augmented Matrix:
rref:
rref:
Solution:
Solution:
2. x – 2y + z = -2
4. x + y – 3z = 1
2x – 3y + 2z = 2
x–z–w=2
4x – 8y + 5z = -5
2x + y – 4z – w = 3
Augmented Matrix:
Augmented Matrix:
rref:
rref:
Solution:
Solution
Find the equation of the parabola, in the form y = ax2 + bx + c, containing the points given.
1. (3, 9), (2, 0), (1,-7)
System of Equations:
Augmented Matrix:
rref:
Solution:
2. (2, -3), (-1, 0), (-3, -18)
System of Equations:
Augmented Matrix:
rref:
Solution: