Explain MATLAB terms and differentiate operators and evaluate MATLAB expressions.

Step 1: Explain MATLAB terms. a) The Command Window* is the primary interface in MATLAB where users type commands and view immediate results. b) The Workspace* is a panel that displays all variables created during a MATLAB session, along with their values and data types. c) The Command History* logs all commands executed in the Command Window, allowing users to recall and reuse previous commands. d) The Current Folder* panel shows the contents of the directory MATLAB is currently working in, including scripts, functions, and data files. Step 2: Differentiate operators and evaluate expressions. a) Unary operators operate on a single operand (e.g., negation -x). Binary operators* operate on two operands (e.g., addition x + y). b)* >> 12 -5 2 This creates a row vector. ans = 12 & -5 & 2 >> 10-62 Following order of operations (multiplication before subtraction): 10 - (6 × 2) = 10 - 12 = -2 ans = -2 >> 5^1/23 Following order of operations (exponentiation, then division and multiplication from left to right): (5^1) / 2 × 3 = 5 / 2 × 3 = 2.5 × 3 = 7.5 ans = 7.5 Step 3: Evaluate MATLAB vector operations. >>pvec = 3:2:10 Creates a vector starting at 3, incrementing by 2, up to 10. pvec = 3 & 5 & 7 & 9 >>pvec(2) = 15 Changes the second element of pvec. pvec = 3 & 15 & 7 & 9 >>pvec(7) = 33 Extends pvec to 7 elements, filling intermediate elements with zeros. pvec = 3 & 15 & 7 & 9 & 0 & 0 & 33 >>pvec([2 4]) Displays elements at indices 2 and 4 of the current pvec. ans = 15 & 9 >>linspace(5,11,3) Generates 3 linearly spaced points between 5 and 11. ans = 5 & 8 & 11 >>logspace(2,4,3) Generates 3 logarithmically spaced points between 10^2 and 10^4. ans = 100 & 1000 & 10000 Step 4: 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. ans = -1 >>mat(2,:) Accesses all elements in the 2nd row. ans = 44 & 9 & 2 >>size(mat) Returns the dimensions of mat. ans = 3 & 3 >>mat(:,4) = [8;11;33] Adds a new 4th column to mat. 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 mat to vector v. v = 5 & -1 & 3 & 33 >>v(2) Accesses the second element of v. ans = -1 >>x = [1 1] Creates a row vector x. x = 1 & 1 >>reshape(mat,2,6) Reshapes mat into a 2x6 matrix, filling elements column-wise from the original mat. ans = 1 & 5 & 9 & 3 & 3 & 11 \\ 44 & 2 & -1 & 2 & 8 & 33 Step 5: 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) y_cos = cos(x); % Calculate cos(x) plot(x, y_sin, 'b-', x, y_cos, 'r--'); % Plot sin(x) in blue solid, cos(x) in red dashed xlabel('x'); % Label for x-axis ylabel('y'); % Label for y-axis title('Plot of sin(x) and cos(x)'); % Title of the plot legend('sin(x)', 'cos(x)'); % Legend for the plots grid on; % Display grid ` The script will produce a plot with two lines: a blue solid line for (x) and a red dashed line for (x) over the specified range. Step 6: Write a MATLAB function for trapezium area. a)* MATLAB function TrapArea: `matlab function area = TrapArea(a, b, h) % TRAPAREA Calculates the area of a trapezium. % area = TRAPAREA(a, b, h