Question
Solve the system of equations
0.6x + 0.8y + 0.1z = 1
1.1x + 0.4y + 0.3z = 0.2
x + y + 2z = 0.5
by LU decomposition method and find the inverse of the coefficient matrix
Answer :
Word Count : 670
__________ ___ __________ ____ ___ _____ ___ _________ ______ _____ __________.
_____ ___ __________ _______ _________ ______ _______ ___.
____ _____ ________ _______ ___ ______ ________ ____ ___.
_______ ____ ______ __________ ______ ________.
_____ __________ ___ ____ ________ _____ _______ __________ __________ ___ _____.
____ ______ ___ ____ ________.
_______ _________ _______ ___ __________ _______ _________.
_____ _____ _______ ______ ________ _____ __________ __________.
____ ____ ______ ____ _______ _________ ______ __________ _________.
_____ ______ ________ __________ ________.
____ _______ ___ ______ _____ ___ ______ ______.
____ ___ __________ _________ __________ _________ ______ ________.
_______ _____ __________ ________ _______ __________ _____ _________.
________ ______ ____ _______ ___ ________ _______ ___ _________ ___.
______ ________ __________ ________ __________ _______.
__________ _______ ____ _____ _________ ___ _______ ___ _____ ____ _______ _____.
______ _________ ___ _________ ____ ________ ____ _________ _____.
_____ __________ _________ ____ ______.
_______ _______ _____ _____ __________ _______ _____ _________ ______.
________ _____ _________ __________ _____ __________ _______ __________ _________.
__________ __________ ___ ____ __________ ___ ________ ______ _________.
_____ _________ __________ ________ ______.
_____ _______ ________ __________ _________ ________.
______ ___ _________ ________ _________ _______ ______ ____ ________ __________ _____ _____.
____ _____ ________ ____ ______ ___ ______ ______ _______.
_________ ________ __________ ____ _________ ______ _________.
_________ _________ ______ ____ _____ _________ ________.
____ ____ _____ ________ ______ _________ ______ __________ _________.
___ _________ __________ ___ ___ _________ ______ ____ __________ _________ ________.
____ ______ ___ ____ ______ ______ ______ ___ _____ __________ __________ _________.
______ _______ ______ ____ ______ ______ __________ __________ _________ _________ ______ _____.
________ _______ _______ __________ ________ _____ ____ ___.
_____ ________ ________ __________ _________ ________.
____ ____ __________ __________ __________ _______ ___ __________ ____ ______ ___ _______.
_________ ____ ___ _______ __________ _________ _____ _________ __________ _________ _____.
_____ ____ ____ _____ _________.
____ __________ ___ _________ __________ _____.
_______ ___ _________ _____ __________ ________ ______ ______ ________ _________ ___ ___.
____ ________ ________ _________ ______ ______ _____ ____ ___ _________ _________.
_____ ______ ________ ___ _______ __________ ______.
___ ________ _______ __________ ______ __________ ___ __________ ______ ______ ___ ___.
____ ______ __________ _________ _______ ______ _________ ________ ____.
___ ________ _______ _____ _______ ______ __________ _______ ______ ___ _________.
___ _________ _________ __________ ____ _____ _____ _____ ___ ____ _____.
__________ ___ ____ ______ __________ ___ ____ ___ _____ ______.
________ ___ ___ ____ _________ ________ ____ _________ _____ _________ _________ _________.
_______ ______ ____ ____ ____ _________.
________ _________ _________ ________ _____.
___ _________ ____ ___ _________ ______.
________ __________ ______ _______ ________ ___ ___.
__________ ______ __________ __________ ______ __________ _______ ___ _______.
________ ___ ________ _______ _______.
______ ______ ________ ______ _______ _______ ______.
__________ ____ ________ ________ ____ _______ _______ ______ ________.
___ ___ ________ _____ ______ ______ ___ ________.
_______ ________ ________ ___ __________ _________ ______ ________ _________ _________.
_______ ___ _________ _____ ________ __________.
Skip in 10
We are given the system: $$ \begin{cases} 0.6x + 0.8y + 0.1z = 1 \\ 1.1x + 0.4y + 0.3z = 0.2 \\ x + y + 2z = 0.5 \end{cases} $$ Coefficient matrix $A$ and vector $b$ are: $$ A = \begin{bmatrix} 0.6 & 0.8 & 0.1 \\ 1.1 & 0.4 & 0.3 \\ 1 & 1 & 2 \end{bmatrix}, \quad b = \begin{bmatrix} 1 \\ 0.2 \\ 0.5 \end{bmatrix} $$ Step 1: LU Decomposition We perform LU decomposition such that $A = LU$, with $L$ lower triangular with 1s on diagonal and $U$ upper triangular. $$ L = \begin{bmatrix} 1 & 0 & 0 \\ l_{21} & 1 & 0 \\ l_{31} & l_{32} & 1 \end{bmatrix}, \quad U = \begin{bmatrix} u_{11} & u_{12} & u_{13} \\ 0 & u_{22} & u_{23} \\ 0 & 0 & u_{33} \end{bmatrix} $$ Step 1a: Set $U$ first row and $L$ first column $$ u_{11} = 0.6, \quad u_{12} = 0.8, \quad u_{13} = 0.1 $$ $$ l_{21} = \frac{1.1}{0.6} = 1.8333, \quad l_{31} = \frac{1}{0.6} = 1.6667 $$ Step 1b: Compute
_______ _________ _____ ________ ______ _______.__________ ___ __________ ____ ___ _____ ___ _________ ______ _____ __________.
_____ ___ __________ _______ _________ ______ _______ ___.
____ _____ ________ _______ ___ ______ ________ ____ ___.
_______ ____ ______ __________ ______ ________.
_____ __________ ___ ____ ________ _____ _______ __________ __________ ___ _____.
____ ______ ___ ____ ________.
_______ _________ _______ ___ __________ _______ _________.
_____ _____ _______ ______ ________ _____ __________ __________.
____ ____ ______ ____ _______ _________ ______ __________ _________.
_____ ______ ________ __________ ________.
____ _______ ___ ______ _____ ___ ______ ______.
____ ___ __________ _________ __________ _________ ______ ________.
_______ _____ __________ ________ _______ __________ _____ _________.
________ ______ ____ _______ ___ ________ _______ ___ _________ ___.
______ ________ __________ ________ __________ _______.
__________ _______ ____ _____ _________ ___ _______ ___ _____ ____ _______ _____.
______ _________ ___ _________ ____ ________ ____ _________ _____.
_____ __________ _________ ____ ______.
_______ _______ _____ _____ __________ _______ _____ _________ ______.
________ _____ _________ __________ _____ __________ _______ __________ _________.
__________ __________ ___ ____ __________ ___ ________ ______ _________.
_____ _________ __________ ________ ______.
_____ _______ ________ __________ _________ ________.
______ ___ _________ ________ _________ _______ ______ ____ ________ __________ _____ _____.
____ _____ ________ ____ ______ ___ ______ ______ _______.
_________ ________ __________ ____ _________ ______ _________.
_________ _________ ______ ____ _____ _________ ________.
____ ____ _____ ________ ______ _________ ______ __________ _________.
___ _________ __________ ___ ___ _________ ______ ____ __________ _________ ________.
____ ______ ___ ____ ______ ______ ______ ___ _____ __________ __________ _________.
______ _______ ______ ____ ______ ______ __________ __________ _________ _________ ______ _____.
________ _______ _______ __________ ________ _____ ____ ___.
_____ ________ ________ __________ _________ ________.
____ ____ __________ __________ __________ _______ ___ __________ ____ ______ ___ _______.
_________ ____ ___ _______ __________ _________ _____ _________ __________ _________ _____.
_____ ____ ____ _____ _________.
____ __________ ___ _________ __________ _____.
_______ ___ _________ _____ __________ ________ ______ ______ ________ _________ ___ ___.
____ ________ ________ _________ ______ ______ _____ ____ ___ _________ _________.
_____ ______ ________ ___ _______ __________ ______.
___ ________ _______ __________ ______ __________ ___ __________ ______ ______ ___ ___.
____ ______ __________ _________ _______ ______ _________ ________ ____.
___ ________ _______ _____ _______ ______ __________ _______ ______ ___ _________.
___ _________ _________ __________ ____ _____ _____ _____ ___ ____ _____.
__________ ___ ____ ______ __________ ___ ____ ___ _____ ______.
________ ___ ___ ____ _________ ________ ____ _________ _____ _________ _________ _________.
_______ ______ ____ ____ ____ _________.
________ _________ _________ ________ _____.
___ _________ ____ ___ _________ ______.
________ __________ ______ _______ ________ ___ ___.
__________ ______ __________ __________ ______ __________ _______ ___ _______.
________ ___ ________ _______ _______.
______ ______ ________ ______ _______ _______ ______.
__________ ____ ________ ________ ____ _______ _______ ______ ________.
___ ___ ________ _____ ______ ______ ___ ________.
_______ ________ ________ ___ __________ _________ ______ ________ _________ _________.
_______ ___ _________ _____ ________ __________.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.
Related Questions
Determine the constants in the differentiation formula
so that the method is of the highest possible order. Find the order and the error term
of the method.
The position f (x) of a particle moving in a line at various times xk is given in the following table. Estimate the velocity and acceleration of the particle at x = 1.2.
| x | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 | 2.2 |
| f(x) | 2.72 | 3.32 | 4.06 | 4.96 | 6.05 | 7.39 | 9.02 |
Find the dominant eigenvalue and the corresponding eigenvector for the matrix
using five iterations of the power method and taking y(10) = [111]T as the initial vector.
The equation x2 + ax + b = 0 has two real roots p and q such that | p | < | q |. If we use the fixed point iteration , to find a root then to which root does it converge?
Find the largest real root α of by f ( x) = x 6 − x − 1 = 0 lying between 1 and 2. Perform three iterations by
i) bisection method
ii) secant method ( x0 = 2, x1 = 1) .
Show that ux = c1eax + c2e-ax is a solution of the difference equation
ux+1 - 2ux cosh .
Solve x3 − 9x + 1 = 0 for the root lying between 2 and 4 by the method of false position. Perform two iterations