The linear equations are defined as follows: 3x - 0.1y - 0.2 z = 7.85 0.1 x + 7y
ID: 3861689 • Letter: T
Question
The linear equations are defined as follows: 3x - 0.1y - 0.2 z = 7.85 0.1 x + 7y - 0.3z = -19.3 0.3x - 0.2y + 10z = 71.4 Use Matlab to apply graphic method to find a root for the f(x). Use Excel to apply bisection method to find a root for the f(x). Use Excel to apply Newton-Raphsen method to find a root for the f(x). Use Matlab to apply Newton-Raphson method to find a root for the f(x). Use Excel to apply Newton-Raphson method to find an optimal point for the f(x) indicating whether it is a max or a min. Convert the linear equations to matrix equation and indicate all the matrices. Use Matlab method to solve the linear equations. Use Cramer's rule to solve the linear equations indicating all the determinants. Use Gauss elimination method either manually or by Matlab to solve the linear equations. Use LU method to solve the linear equations indicating L and U.Explanation / Answer
A=
3
-0.1
-0.2
0.1
7
-0.3
0.3
-0.2
10
B =
x
y
z
C =
7.85
-19.3
71.4
Such that A . B = C,
Now, we first consider A matrix and and convert it to row echelon form using Gauss Elimination Method.
R2 = R2 - (1/30)R1
R3 = R3 - (1/10) R1
Then we get A =
3
-0.1
-0.2
0
7.003
-0.293
0
-0.19
10.02
Again applying R3 = R3 + (1/36.857)R2
Then we get A =
3
-0.1
-0.2
0
7.003
-0.293
0
0
10.012
So ,
U=
3
-0.1
-0.2
0
7.003
-0.293
0
0
10.012
L =
1
0
0
0.03
1
0
0.1
-0.027
1
Now, L . U . B = C
We consider U . B = Z
Hence solving L . Z = C
Let Z =
z1
z2
z3
On solving ,
z1 = 7.85
0.03*z1 + z2 = -19.3, on substituting the value of z1 we get z2 = -19.5355
0.1*z1 - 0.027 * z2 + z3 = 71.4
On substituting the value of z1 and z2, we get z3 = 70.08
Now we solve
U . B = Z, the following equations are formed:
3x-0.1y-0.2z = 7.85
7.003y-0.293z = -19.5355
10.012z = 70.08
On solving the equations, we obtain
X = 3
Y = -2.50
Z = 6.99 (approx 7)
3
-0.1
-0.2
0.1
7
-0.3
0.3
-0.2
10
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