admin So far you have learned about non-homogeneous system of linear equations of the form where is the augmented matrix and is the matrix representing unknowns and is the result of the product. The homogeneous system of linear equations has all of its constant term set to zero. Consider the following homogeneous system of linear equation. … Read more
Matrix has a special function called trace function. If is a square matrix then the sum of its main diagonal entry is called trace of matrix and is denoted by . Let be a square matrix with size , then The trace of matrix is, Let is see few examples of traces of matrices. Example … Read more
The transpose of a matrix is denoted by is obtained by changing rows into columns or columns to rows of a matrix . If size of the matrix is then the size of the transposed matrix is . Transpose Of A Matrix The element in row and column of matrix becomes the row and column … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more
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. … Read more
The hash table is perfect solution to store dictionary where each data is uniquely identified using a key. The dictionaries are implemented using arrays. The key are stored with the object itself and each data element has its own index value. Therefore, data is stored in the array as key-value pair. The hash table uses … Read more
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