Augmented Matrix
A matrix formed by combining columns of two matrices is called Augmented Matrix. An augmented matrix is used to perform elementary row operations, solve a linear equation, and find the inverse of a matrix. Let us understand through an example.
Let’s say we have a matrix A = [Tex]\begin{bmatrix} a_1 & b_1 & c_1\\ a_2 & b_2 & c_2\\ a_3 & b_3 & c_3 \end{bmatrix}[/Tex], X = [Tex]\begin{bmatrix} x \\ y \\z \end{bmatrix}[/Tex]and B = [Tex]\begin{bmatrix} p_{1} \\ p_{2} \\p_{3} \end{bmatrix}[/Tex]then augmented matrix is formed between A and B. The augmented matrix for A and B is given as
[A|B] = [Tex]\left[\begin{array}{lll|l} a_1 & b_1 & c_1&p_1\\ a_2 & b_2 & c_2&p_2\\ a_3 & b_3 & c_3 &p_3\end{array}\right][/Tex]
Matrices
Matrix is a rectangular array of numbers, symbols, points, or characters each belonging to a specific row and column. A matrix is identified by its order which is given in the form of rows ⨯ and columns. The numbers, symbols, points, or characters present inside a matrix are called the elements of a matrix. The location of each element is given by the row and column it belongs to.
Matrices are important for students of class 12 and also have great importance in engineering mathematics as well. In this introductory article on matrices, we will learn about the types of matrices, the transpose of matrices, the rank of matrices, the adjoint and inverse of matrices, the determinants of matrices, and many more in detail.
Table of Content
- What are Matrices?
- Order of Matrix
- Matrices Examples
- Operation on Matrices
- Addition of Matrices
- Scalar Multiplication of Matrices
- Multiplication of Matrices
- Properties of Matrix Addition and Multiplication
- Transpose of Matrix
- Trace of Matrix
- Types of Matrices
- Determinant of a Matrix
- Inverse of a Matrix
- Solving Linear Equation Using Matrices
- Rank of a Matrix
- Eigen Value and Eigen Vectors of Matrices
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