Solve the system of equations
with partial pivoting. Store the multipliers and also write the pivoting vectors.
To solve the given system of equations using Gaussian elimination with partial pivoting, let's first write the system in matrix form: \[ \begin{bmatrix} 3 & 2 & 4 \\ 2 & 1 & 1 \\ 1 & 3 & 5 \end{bmatrix} \begin{bmatrix} ________ ________ _______ _______ ______ _________ ________.
___ ___ __________ ____ _______ _____ __________ _______ _________ __________.
______ _____ ______ ___ ______ ________ _____ ___ ______ __________.
____ ________ ___ ____ ____ _____ ____ _______ ______ __________ __________.
__________ ___ ___ _________ ___ ______ ________ ___ _____ ________.
___ _________ __________ _________ ____ ______ _____.
_______ _______ ___ ___ ____ _____ ______ _____ _____ _______ __________ __________.
______ ____ ___ ________ ___ _______ _____.
_____ __________ ____ ________ _____ ____ _____ __________.
_____ ___ _______ __________ ___ _______ ___ ______.
____ __________ _________ _____ ___ ________ ___ ______ ____.
______ _____ ________ ____ ____.
____ ______ ____ ______ _________ _______ ___ ____ _______ ______ _____.
_____ _____ __________ ________ __________ _________ ______.
____ ____ _______ _______ _________ ______ __________ ______ _____ ___ __________.
_________ _________ _________ ___ __________ ______ ___ ______ __________ ______ _______ ___.
_______ __________ __________ ___ ______ ____.
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_________ __________ ________ ____ ________ _________ ____ ______ _____ ___.
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Find by Newton’s method the roots of the following equations correct to three places of decimals
i)
ii)
A table of values is to be constructed for the function f (x) given by in the interval [1, 4] with equal step length. Determine the spacing h such that quadratic interpolation gives result with accuracy
.
Derive a suitable numerical differentiation formula of 0(h2) to find (2.4) with h= 0.1 given the table
| x | 0.1 | 1.2 | 2.4 | 3.9 |
| 3.41 | 2.68 | 1.37 | -1.48 |
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 |
Using as an initial approximation find an approximation to one of the zeros of
by using Birge-Vieta method. Perform two iterations.
Find the inverse of the matrix
using Gauss Jordan method.
Solve the system of equations
by LU decomposition method and find the inverse of the coefficient matrix