Matrix Calculations

Matrix Calculations

Basic Matrix Operations

• Addition/Subtraction: Matrices can be added or subtracted element by element. The matrices must be the same size.
• Scalar Multiplication: Each element of the matrix is multiplied by a constant.
• Matrix Multiplication: The element at the i-th row and j-th column of the resultant matrix is the sum of products of elements from the i-th row of the first matrix and the j-th column of the second matrix.

Properties of Matrix Operations

• Commutative Property: Matrix addition is commutative, but matrix multiplication is not.
• Associative Property: Both matrix addition and multiplication are associative.
• Distributive Property: Matrix multiplication over addition follows the distributive rule.

Determinants and Inverse Matrices

• The determinant of a matrix is a special number that can be calculated from a square matrix.
• A matrix has an inverse only if its determinant is not zero. Inverse of Matrix A is denoted as A^-1.
• The product of a matrix and its inverse is the identity matrix.

Matrix Transpose

• The transpose of a matrix is found by swapping rows with columns.

Applications of Matrices

• Matrices are used to solve systems of linear equations.
• They are also used to perform transformations in geometry.

Remember, practicing matrix calculations on a range of different function types is the key part of mastering this topic. Use past paper questions to apply these rules in different contexts.