Use the Gauss elimination method to solve the system of equations:
x1 - 2x2 + x3 = 0 ; 2x1 + x2 - 3x3 = 5 ; 4x1 -7x2 + x3 = -1
To solve the system of equations using Gauss elimination, we represent the system in augmented matrix form:
\[
\begin{bmatrix}
1 & -2 & 1 & | & 0 \\
2 & 1 & -3 & | & 5 \\
4 & -7 & 1 & | & -1
\end{bmatrix}
\]
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In what way is the Newton-Raphson method more beneficial than the bisection method?
The approximate value of the derivative of a function f(x)at x can be calculated using the
formula:
Calculate for
and (ii) h = 0.05.
Determine the true error and relative true error in each case.
Given the following data for the velocity as a function of time, calculate the velocity at t = 12 s using second order polynomial interpolation in the Newton divided difference method:
| Time (in s) | 0 | 15 | 18 | 22 | 24 |
| Velocity (in ms-1) | 20 | 25 | 35 | 30 | 80 |
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Define true error and relative true error.
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