Matrices

Matrices are key concepts in mathematics, widely used in solving equations and problems in fields like physics and computer science. A matrix is simply a grid of numbers, and a determinant is a value calculated from a square matrix.

Example: [Tex]\begin{bmatrix} 6 & 9 \\ 5 & -4 \\ \end{bmatrix}_{2\times 2}[/Tex], [Tex]\begin{bmatrix} 3 & -4 & 5 \\ 1 & 7 & 6 \\ 6 & -2 & 9 \\\end{bmatrix}_{3 \times3}[/Tex]

Matrices for School Students & Beginners

• Introduction to Matrix
• Types of Matrices
• Operations on Matrices
  • Matrix Addition
  • Matrix Subtraction
  • Matrix Multiplication by a Scalar
  • Matrices Multiplication
  • Transpose of a Matrix
• Determinant of a Matrix
• Properties of Determinants
• Determinant of a Matrix Formula
• Invertible Matrix
• Inverse of a Matrix
• Methods to Find Inverse of a Matrix
• How to Solve a System of Equations using Inverse of Matrices
• Transformation Matrix
• Solve Systems of Equations Using Matrices
• Augmented Matrix
• Real life application of Matrices

Practice Questions on Matrices

• Matrix Formulas
• Practice Questions on Matrix Multiplication
• Practice Questions on Matrices

Advanced Topics on Matrices

• Rank of Matrix
• Trace of Matrix
• Cramer’s Rule
• Covariance Matrix
• Eigen Decomposition of a Matrix
• Eigenvalues and Eigenvectors
• Partition Matrix

Matrices for Programmers

• Matrix Operations
• Rotate Matrix Clockwise
• Sort the given matrix
• Program to multiply two matrices
• Find the row with maximum number of 1s
• Boundary elements of a Matrix
• Check if a matrix is a Toeplitz Matrix
• Print a given matrix in spiral form
• Zigzag (or diagonal) traversal of Matrix
• Spiral Traversal of Matrix
• Search in a Row-wise and Column-wise Sorted Matrix
• Find the number of islands
• Maximum sum rectangular submatrix in a given matrix
• Minimum Initial Points to Reach Destination
• Count number of paths with at-most k turns
• Matrix Chain Multiplication

Matrices – FAQs

What is a matrix and its determinants?

Matrix is a rectangular array of numbers, symbols, points, or characters each belonging to a specific row and column it is identified by its order which is given in the form of rows ⨯ and columns.. And Determinant of a square matrix is the scalar value or number calculated using the square matrix. The determinant of square matrix X is represented as |X| or det(X).

What is a Diagonal Matrix?

A square matrix in which all non-diagonal elements are zero is called a Diagonal Matrix.

What is transpose of a matrix?

The transpose of a matrix is a new matrix formed by swapping its rows and columns. In other words, the element at the position (row, column) in the original matrix moves to the position (column, row) in the transposed matrix.

What is the Formula to find the Inverse of a Matrix?

The inverse of the matrix can be find out using the formula A^-1 = (1/|A|)(adj A)

What are Invertible Matrices?

The matrices whose inverse exist are called invertible. Invertible matrices are matrices that have a non-zero determinant.

kartik

Follow

Improve

Article Tags :

• Class 12
• Engineering Mathematics
• GATE CS
• Mathematics
• School Learning
• Maths-Class-12
• Matrix and Determinant

+3 More