https://file.aiquickdraw.com/mathbot/file/1727278574642ey0satfm.jpeg

https://file.aiquickdraw.com/mathbot/file/1727278574642h8g3r3mm.png

Let's break down the content from both the whiteboard and the assignment.

### Whiteboard Image Overview:
The image on the whiteboard contains a mixture of beam analysis and bending moment calculations. Here's a structured breakdown:

1. **Beam Diagrams and Force Systems:**
   - The top section seems to be analyzing different types of loading conditions on beams: distributed loads (e.g., 4kN/m) and point loads.
   - Reaction forces at points, such as \( R_v = 13.8 \, \text{kN} \), are calculated.
   - Several segments indicate different spans and loading positions.
   
2. **Shear Force and Bending Moment Diagrams:**
   - The second part has the shear force diagrams for different points along the beam (e.g., 0 to 8 m, and 8 to 13 m).
   - Below that are the corresponding bending moment diagrams for the same segments.

3. **Equilibrium and Structural Equations:**
   - Various structural and equilibrium conditions are being applied (e.g., \( \sum F = 0 \), \( \sum M = 0 \)).
   - Several algebraic steps involving the positions of loads and reactions are calculated (for instance, \( x = 0 \), \( x = 8 \)).

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### Assignment Image Overview:
This is an assessment question from Politeknik Sultan Salahuddin Abdul Aziz Shah, focusing on linear algebra and numerical methods.

#### 1) Linear System and Doolittle Method:
   - **Given system of equations:**
     \[
     \begin{aligned}
     v - 3i &= 8 - 2r \\
     4v - i - r &= 9 \\
     3v + 2i + r &= 21
     \end{aligned}
     \]
   - The tasks include:
     - Matrix formulation \( A \mathbf{x} = B \)
     - LU decomposition using Doolittle's method.
     - Calculate the values of \( v \), \( i \), and \( r \).

#### 2) Fixed-Point Iteration:
   - The problem focuses on the equation \( x^4 - x = 10 \).
   - The task is to use the **Fixed-Point Iteration Method** to find the root of the function with an initial guess \( x_0 = 1.75 \), and obtain a result accurate to two decimal places.

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### Do you need assistance with any specific parts from the whiteboard (like the beam analysis) or would you like a detailed step-by-step solution for the assignment problems (e.g., LU decomposition or Fixed-Point Iteration)? 

Here are a few questions you might find interesting:

1. How are shear force and bending moment diagrams related in beam analysis?
2. What is the significance of LU decomposition in solving linear systems?
3. How does the Doolittle method help in factorizing matrices?
4. What is the Fixed-Point Iteration Method, and why is it used in solving nonlinear equations?
5. How does choosing an initial guess affect convergence in numerical methods?

**Tip:** In beam analysis, always ensure to check for both equilibrium conditions and compatibility to avoid inconsistencies in shear force or bending moment calculations.

An experiment to measure resistance produces a set of the following linear equations: v - 3i = 8 - 2r, 4v - i - r = 9, 3v + 2i + r = 21. Solve the system using matrix methods (LU decomposition) and numerical methods (Fixed-Point Iteration).

Learn how to solve a system of linear equations using LU decomposition and numerical methods like Fixed-Point Iteration. This problem involves applied mathematics and is suitable for college-level engineering students.

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