Question

The following set of simultaneous equations represents the relationship between 3 soil stresses x, y and z. Convert these equations into matrix format and using Gaussian elimination determine the values of x, y and z.

x + 2y – 3z = 3

2x – y – z = 11

3x + 2y + z = -5

Answer #1

1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

Matlab: Solve the following set of simultaneous equations.
Remember, the system cannot be solved if the determinant of the
coefficient matrix is zero. Use if statements to only display the
results if the determinant is not zero
a) 3x1 + 2x2 + 4x3 = 5
2x1 + 5x2 + 3x3 = 17
7x1 + 2x2 + 2x3 = 11
b) x – y – z = 0
30x + 40y = 12
30x + 50z = 12
c) 4x +...

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

solve the following pairs of simultaneous equations
a) x=7y+3
y=3x-7
b) 2x+5y =23
5x-2y=14

3) For the given system of equations:
x+y-z=-6
x+2y+3z=-10
2x-y-13z=3
Rewrite the system as an augmented matrix. [4 pt]
Find the reduced row echelon form of the matrix using your
calculator, and write it in the spacebelow. [4 pt]
State the solution(s) of the system of equations. [3 pt]

Consider the following linear system:
x + 2y + 3z = 6
2x - 3y + 2z = 14
3x + y - z = -2
Use Gaussian Elimination with Partial Pivoting to
solve a solution in an approximated sense.

Solve each system of equations
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10

Section B.3 - Algebra - Simultaneous and Quadratic Equations
Solve problems 1 and 2 using the comparison, elimination, or
substitution method.
1) x +y =2 2x -3y =5
2 ) 3x - 5y=5 7x + y = 75

1) Solve these equations: 3x-y=-11
x+2y=8
2) Solve these equations:
x+y+z=6
x-y-z=-4
2x+y-4z=-8

Use Gauss-Jordan method (augmented matrix method) to
solve the following systems of linear equations. Indicate whether
the system has a unique solution, infinitely many solutions, or no
solution. Clearly write the row operations you use. (a) (5 points)
x + y + z = 6 2x − y − z = 3 x + 2y + 2z = 0 (b) (5 points) x − 2y
+ z = 4 3x − 5y + 3z = 13 3y − 3z =...

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