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# Matrix determinant, Cramer's rule, Gaussian elimination

1). Write the matrix in reduced row-echelon form: [1, 2, -1, 3], [7, -1, 0, 2], [3, 2, 1,-1].

2) Find the equation of the parabola that passes through the given points. Use the graphing utility to verify your result. (Please look at the picture).

3) Use a graphing utility to find AB, given. A= [1, 3, 6], [4, 1, 3] B= [0, 1, 6], [3, -1, 1], [5, 2, 3]

4) Given A = [1, 0, 3], [-1, 2, -2], [1, 1, 2] and B = [1, 1, 0], [3, 1, 2], [-1, 1, -1] find BA.

5) Given A = [1, 5, -1], [2, 3, -2], [-1, -4, 3] find A^-1

6) Use a graphing utility to solve (if possible) the system of linear equations.
5x+y+2z=0
x-3z=-2
2x+y+z=6

7) Find the determinant of the matrix: [3, 0, 1], [-1, 4, -1], [5, -2, 0]

8) Evaluate the determinant: (Please look at pictures)

9) If A= [2, -1], [-3, 4] and B= [-2, 0], [-1, 3], find C if A+C=2B

10) Use Cramer's rule to solve the system of linear equation.
5x+5y+4z=4
10x-5y+2z=11
5x-5y+2z=7

11) Solve the system graphically:
x^2+y^2=25
x-y=1

12) Solve the system by method of substitution:
y=1/x
x+5y=6

13) Solve this system by method of elimination and verifying the solution with a graphing utility:
2x-5y= -4
4x+3y=5

14) How many liters of 40% solution of acid must be combined with a 15% solution to obtain 30 liters of a 20% solution?

15) Use Gaussian elimination to solve the system of equations:
x+2y+z=6
2x-y+3z=-2
x+y-2z=0

#### Solution Summary

Equation of the parabola is denoted. The Matrix determinants, Cramer's rule and Gaussian elimination are analyzed.

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