linear algebra

Matrix Multiplication

The multiplication of matrices means rows of matrix is multiplied to columns of to obtain a third matrix . We also evaluate the matrix multiplication with respect to fundamental properties of mathematics such as commutative, associative property, identity property. Conditions for Matrix Multiplication If and are two matrices with sizes and respectively. The following conditions …

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Matrix Subtraction

In the previous post, you have learned about matrix addition and its mathematical properties. The matrix subtraction is also mathematical operation on two matrices where elements of right hand matrix is subtract from elements of matrix on the left hand. The result is stored in a separate third matrix. Condition To Subtract Matrices Similar to …

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Matrix Addition

Previous article, you learned that matrix are two dimensional representation of data other than augmented matrix from a system of linear equations. Matrix operations such as addition is possible because you can add two matrices and by simply adding their corresponding elements which will give a thrid matrix as a result. Condition To Add Two …

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Matrix Operations

In this section, you will learn common mathematical operations performed on matrices. These operations range from common arithmetic operations such as addition, subtraction, multiplication to transpose matrices. Before we proceed to learn about matrix operations, you should learn common matrix notations and terminologies used in this section. Common Matrix Notations An augmented matrix is derived …

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Gaussian Elimination

Gaussian elimination is a technique to change the augmented matrix into a row echelon form.There are many echelon forms, but subsequently, we must find the reduced row echelon form. The reduced row echelon form can can be achieved through another technique called the Gauss-Jordan elimination technique. Augmented Matrix To Row Echelon Form Given an augmented …

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Row Echelon Form

Previously, you learned about deriving an augmented matrix from a system of linear equations. You have also learned about reducing the augmented matrix into a simpler equivalent matrix that is easy to solve through series of row operations on the matrix. This kind of matrix form is known as the row echelon form of matrix. …

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