Differentiate between unary and binary operators and evaluate expressions.

• a) Unary operators act on a single operand. An example is the negation operator, such as -x, where - operates only on x. Binary operators act on two operands. Examples include arithmetic operators like addition x + y or subtraction x - y, where the operator acts on both x and y.
• b) Evaluate the MATLAB statements:
  • >> 12 -5 2 This statement creates a row vector with the given elements. $$\text{ans} = \begin{bmatrix} 12 & -5 & 2 \end{bmatrix}$$
  • >> 10-6*2 Following the order of operations (multiplication before subtraction): $$10 - (6 \times 2) = 10 - 12 = -2$$ $$\text{ans} = -2$$
  • >> 5^1/2*3 Following the order of operations (exponentiation first, then division and multiplication from left to right): $$(5^1) / 2 \times 3 = 5 / 2 \times 3 = 2.5 \times 3 = 7.5$$ $$\text{ans} = 7.5$$

• >>pvec = 3:2:10 Creates a row vector starting at 3, incrementing by 2, up to 10. $$\text{pvec} = \begin{bmatrix} 3 & 5 & 7 & 9 \end{bmatrix}$$
• >>pvec(2) = 15 Changes the second element of pvec to 15. $$\text{pvec} = \begin{bmatrix} 3 & 15 & 7 & 9 \end{bmatrix}$$
• >>pvec(7) = 33 Extends pvec to 7 elements. Elements between the last existing element (index 4) and the new element (index 7) are filled with zeros. $$\text{pvec} = \begin{bmatrix} 3 & 15 & 7 & 9 & 0 & 0 & 33 \end{bmatrix}$$
• >>pvec([2 4]) Displays the elements of pvec at indices 2 and 4. $$\text{ans} = \begin{bmatrix} 15 & 9 \end{bmatrix}$$
• >>linspace(5,11,3) Generates 3 linearly spaced points between 5 and 11 (inclusive). $$\text{ans} = \begin{bmatrix} 5 & 8 & 11 \end{bmatrix}$$
• >>logspace(2,4,3) Generates 3 logarithmically spaced points between $10^2$ and $10^4$ (inclusive). $$\text{ans} = \begin{bmatrix} 100 & 1000 & 10000 \end{bmatrix}$$

• >>mat = [1:3; 44 9 2; 5 -1 3] Creates a 3x3 matrix. $$\text{mat} = \begin{bmatrix} 1 & 2 & 3 \\ 44 & 9 & 2 \\ 5 & -1 & 3 \end{bmatrix}$$
• >>mat(3,2) Accesses the element in the 3rd row, 2nd column of mat. $$\text{ans} = -1$$
• >>mat(2,:) Accesses all elements in the 2nd row of mat. $$\text{ans} = \begin{bmatrix} 44 & 9 & 2 \end{bmatrix}$$
• >>size(mat) Returns the dimensions of mat (rows, columns). $$\text{ans} = \begin{bmatrix} 3 & 3 \end{bmatrix}$$
• >>mat(:,4) = [8;11;33] Adds a new 4th column to mat with the specified values. $$\text{mat} = \begin{bmatrix} 1 & 2 & 3 & 8 \\ 44 & 9 & 2 & 11 \\ 5 & -1 & 3 & 33 \end{bmatrix}$$
• >>numel(mat) Returns the total number of elements in mat (3 rows $\times$ 4 columns = 12 elements). $$\text{ans} = 12$$
• >>v = mat(3,:) Assigns the 3rd row of the current mat to a new vector v. $$\text{v} = \begin{bmatrix} 5 & -1 & 3 & 33 \end{bmatrix}$$
• >>v(2) Accesses the second element of vector v. $$\text{ans} = -1$$
• >>v(1) = [] Deletes the first element of vector v. $$\text{v} = \begin{bmatrix} -1 & 3 & 33 \end{bmatrix}$$
• >>reshape(mat,2,6) Reshapes the current mat (which is 3x4, having 12 elements) into a 2x6 matrix. Elements are filled column-wise from the original matrix. $$\text{ans} = \begin{bmatrix} 1 & 5 & 9 & 3 & 3 & 11 \\ 44 & 2 & -1 & 2 & 8 & 33 \end{bmatrix}$$

% MATLAB script to plot sin(x) and cos(x)
x = linspace(0, 2*pi, 100); % Generate 100 points from 0 to 2*pi
y_sin = sin(x);             % Calculate sin(x) for each point in x
y_cos = cos(x);             % Calculate cos(x) for each point in x

% Plot sin(x) as a blue solid line and cos(x) as a red dashed line
plot(x, y_sin, 'b-', x, y_cos, 'r--');
xlabel('x');                        % Label for the x-axis
ylabel('y');                        % Label for the y-axis
title('Plot of sin(x) and cos(x)'); % Title of the plot
legend('sin(x)', 'cos(x)');         % Legend to identify the lines
grid on;                            % Display a grid on the plot

This script will generate a 2D plot showing the sine and cosine functions over the specified range.

• a) MATLAB function TrapArea: Create a file named TrapArea.m with the following content:

  function area = TrapArea(a, b, h)
  % TRAPAREA Calculates the area of a trapezium.
  %   area = TRAPAREA(a, b, h) calculates the area of a trapezium
  %   with parallel sides 'a' and 'b', and height 'h'.
  
  area = 0.5 * (a + b) * h;
  end
  

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  To use this function, you would call it from the Command Window, for example: >> myArea = TrapArea(5, 7, 3) $$\text{myArea} = 18$$
• b) Repeat the process using an anonymous function: An anonymous function can be defined directly in the Command Window or a script.

  TrapArea_anon = @(a, b, h) 0.5 * (a + b) * h;
  

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  To use this anonymous function, you would call it like a regular function: >> myArea_anon = TrapArea_anon(5, 7, 3) $$\text{myArea\_anon} = 18$$