Differentiate between unary and binary operators and evaluate expressions.

Step 1: 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. ans = 12 & -5 & 2 >> 10-62 Following the order of operations (multiplication before subtraction): 10 - (6 × 2) = 10 - 12 = -2 ans = -2 >> 5^1/23 Following the order of operations (exponentiation first, then division and multiplication from left to right): (5^1) / 2 × 3 = 5 / 2 × 3 = 2.5 × 3 = 7.5 ans = 7.5 Step 2: Evaluate MATLAB vector operations. >>pvec = 3:2:10 Creates a row vector starting at 3, incrementing by 2, up to 10. pvec = 3 & 5 & 7 & 9 >>pvec(2) = 15 Changes the second element of pvec to 15. pvec = 3 & 15 & 7 & 9 >>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. pvec = 3 & 15 & 7 & 9 & 0 & 0 & 33 >>pvec([2 4]) Displays the elements of pvec at indices 2 and 4. ans = 15 & 9 >>linspace(5,11,3) Generates 3 linearly spaced points between 5 and 11 (inclusive). ans = 5 & 8 & 11 >>logspace(2,4,3) Generates 3 logarithmically spaced points between 10^2 and 10^4 (inclusive). ans = 100 & 1000 & 10000 Step 3: Evaluate MATLAB matrix operations. >>mat = [1:3; 44 9 2; 5 -1 3] Creates a 3x3 matrix. mat = 1 & 2 & 3 \\ 44 & 9 & 2 \\ 5 & -1 & 3 >>mat(3,2) Accesses the element in the 3rd row, 2nd column of mat. ans = -1 >>mat(2,:) Accesses all elements in the 2nd row of mat. ans = 44 & 9 & 2 >>size(mat) Returns the dimensions of mat (rows, columns). ans = 3 & 3 >>mat(:,4) = [8;11;33] Adds a new 4th column to mat with the specified values. mat = 1 & 2 & 3 & 8 \\ 44 & 9 & 2 & 11 \\ 5 & -1 & 3 & 33 >>numel(mat) Returns the total number of elements in mat (3 rows × 4 columns = 12 elements). ans = 12 >>v = mat(3,:) Assigns the 3rd row of the current mat to a new vector v. v = 5 & -1 & 3 & 33 >>v(2) Accesses the second element of vector v. ans = -1 >>v(1) = [] Deletes the first element of vector v. v = -1 & 3 & 33 >>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. ans = 1 & 5 & 9 & 3 & 3 & 11 \\ 44 & 2 & -1 & 2 & 8 & 33 Step 4: Write a MATLAB script to plot (x) and (x). `matlab % MATLAB script to plot sin(x) and cos(x) x = linspace(0, 2pi, 100); % Generate 100 points from 0 to 2pi 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. Step 5: Write a MATLAB function for trapezium area. a)* MATLAB function TrapArea: Create a file named TrapArea.m with the following content: `matlab 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 ` To use this function, you would call it from the Command Window, for example: >> myArea = TrapArea(5, 7, 3) myArea = 18 b)* Repeat the process using an anonymous function: An anonymous function can be defined directly in the Command Window or a script. `matlab TrapArea_anon = @(a, b, h) 0.5 (a + b) h; ` To use this anonymous function, you would call it like a regular function: >> myArea_anon = TrapArea_anon(5, 7, 3) myArea\_anon = 18 3 done, 2 left today. You're making progress.