JNTU B.Tech IV MATLAB APPLICATIONS Previous Question Paper (December - 2020 - R15)

MATLAB supports various arithmetic operations that can be performed on scalars, vectors, and matrices. These operations are categorized into array operations (element-by-element) and matrix operations (linear algebraic).

1. Basic Scalar Arithmetic: These operations are performed using standard operators: addition (+), subtraction (-), multiplication (*), division (/), left division (\), and exponentiation (^).

2. Array (Element-by-Element) Operations: When working with vectors or matrices, adding a period (.) before the operator forces element-wise calculation. This is essential for multiplication, division, and exponentiation.

• Element-wise Multiplication (.*): Multiplies corresponding elements of two arrays of the same size.
  A = [1 2]; B = [3 4]; C = A .* B; % Result: [3 8]
• Element-wise Division (./): Divides corresponding elements.
  D = B ./ A; % Result: [3 2]
• Element-wise Power (.^): Raises each element to the specified power.
  E = A .^ 2; % Result: [1 4]

3. Matrix Operations: These follow the rules of linear algebra. The standard operators (*, /, ^) perform matrix multiplication, matrix division, and matrix exponentiation respectively.

• Matrix Multiplication (*): The number of columns in the first matrix must equal the number of rows in the second.
  M1 = [1 2; 3 4]; M2 = [5 6; 7 8]; M3 = M1 * M2;
• Matrix Division (\ and /): Used to solve linear systems of equations. A \ B is equivalent to solving the system Ax = B for x, computed as inv(A)*B.
• Matrix Power (^): Computes the matrix raised to an integer power (e.g., A^2 is A*A).

4. Transpose Operator: The single quote (') is used to compute the complex conjugate transpose of a matrix, while the dot-transpose (.') performs a simple transpose without conjugation.

MATLAB provides a comprehensive suite of built-in functions for creating, manipulating, and analyzing arrays. These functions are categorized based on their primary utility:

1. Array Creation Functions:

• zeros(m,n): Creates an m-by-n matrix of zeros. Example: A = zeros(2,3) creates a 2x3 matrix of zeros.
• ones(m,n): Creates an m-by-n matrix of ones. Example: B = ones(3,2) creates a 3x2 matrix of ones.
• eye(n): Creates an n-by-n identity matrix. Example: I = eye(3) creates a 3x3 identity matrix.
• rand(m,n): Creates an m-by-n matrix with uniformly distributed random numbers between 0 and 1.

2. Array Manipulation Functions:

• reshape(A,m,n): Changes the dimensions of array A to m-by-n without changing the data. Example: B = reshape(A, 2, 4) converts an 8-element vector into a 2x4 matrix.
• transpose(A) or A': Flips the matrix over its diagonal, swapping rows and columns.
• fliplr(A) / flipud(A): Flips the array horizontally (left-right) or vertically (up-down).
• cat(dim, A, B): Concatenates arrays along the specified dimension.

3. Inquiry and Statistical Functions:

• size(A): Returns a vector containing the number of rows and columns in A.
• length(A): Returns the length of the largest array dimension.
• sum(A): Returns the sum of elements in each column.
• mean(A): Calculates the average value of elements in each column.
• max(A) / min(A): Returns the maximum or minimum value in each column.

4. Search and Logical Functions:

• find(A > x): Returns the linear indices of elements in A that satisfy the condition A > x.
• sort(A): Sorts the elements of each column in ascending order.