Help please! Given the following system of equations -3X2+7x3= 2 x1 + Zx2- X3 =
ID: 1862988 • Letter: H
Question
Help please!
Given the following system of equations -3X2+7x3= 2 x1 + Zx2- X3 = 5x1 - 2x2 = 2 Compute the determinant of the matrix for this system manually Solve for xi, X2 and xj using the inverse matrix multiplication method with MATLAB. Check your results by substituting the results back into the three equations For the given system of equations: X1 + 2x2- X4 = 9 2xi+ 3x2 -x3- 9 4x2 + 2x3 - 5x4 = 26 5xi + 5x2 + 2x3 - 4x4 = 32 Determine K and r for the system of equations, Kx = r, where K is the system matrix, r is the vector of the right hand sides of the rows. Compute the determinant and rank of K Compute the vector x for this system of equations with the backslash operator. Change the first equation in the system to 1Oxl +10x2 + 4x3 - 8x4 = 9; then repeat (b) and (c). Comment on the outcomes.Explanation / Answer
Q6a
A =
0 -3 7
1 2 -1
5 -2 0
it is the matrix for the first part
it's determinant= (use det(A) in matlab=-69) and manually
it is 0(0*-2--2*-1)-1(-3*-1--2*7)+5*(-3*-1-2*-7) = -69
Q6b
x =
0.9855
1.4638
0.9130
use
B =
2
3
2
x=AB
Q6c
on putting into the solution (values satisfies the equation)
-3x2+7x3=2..... till 3rd question
Q7a
K =
1 2 0 -1
2 3 -1 0
0 4 2 -5
5 5 2 -4
r =
9
9
26
32
Q7b
det(K)=3
rank K=4(no. of independent rows/columns)
Q7 C
x =
1.0000
3.0000
2.0000
-2.0000
x=K
Q7d
K =
10 10 4 -8
2 3 -1 0
0 4 2 -5
5 5 2 -4
det(K)=0
rank K=3(no. of independent rows/columns)
on using backslach function we get:
x=K
Warning: Matrix is singular
to working precision.
x =
NaN
NaN
Inf
Inf
which physically infers that there in no solution for a given particular sets of equation as 2 lines are parallel to each other
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