Explain the difference between element-wise multiplication (.*), matrix multiplication (*), and dot product (dot()) operations in MATLAB, and provide an example scenario where each operation would be used.

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Answered by suresh

Difference Between Element-wise Multiplication, Matrix Multiplication, and Dot Product Operations in MATLAB

The Difference Between Element-wise Multiplication, Matrix Multiplication, and Dot Product Operations in MATLAB

Element-wise multiplication in MATLAB is carried out using the .* operator. It performs multiplication of corresponding elements in two arrays or matrices.

Matrix multiplication in MATLAB is denoted by the * operator. It multiplies the rows of the first matrix with the columns of the second matrix to produce a new matrix.

The dot product operation in MATLAB is performed using the dot() function. It computes the sum of the products of corresponding elements in two arrays or vectors.

Examples:

Element-wise Multiplication:

Scenario: Calculating element-wise product of two matrices.


A = [1 2; 3 4];
B = [5 6; 7 8];
C = A .* B;

In this scenario, each element of matrix A is multiplied with the corresponding element in matrix B.

Matrix Multiplication:

Scenario: Performing matrix multiplication of two matrices.


A = [1 2; 3 4];
B = [5 6; 7 8];
C = A * B;

Here, the rows of matrix A are multiplied with the columns of matrix B to obtain the resulting matrix C.

Dot Product:

Scenario: Calculating the dot product of two vectors.


A = [1 2 3];
B = [4 5 6];
C = dot(A, B);

The dot product operation computes the sum of the products of the corresponding elements in vectors A and B.

Answer for Question: Explain the difference between element-wise multiplication (.*), matrix multiplication (*), and dot product (dot()) operations in MATLAB, and provide an example scenario where each operation would be used.