In linear algebra, matrix inverse holds a special place because there is no division in matrix algebra. You cannot divide two matrices. Fortunately, the division is possible when a matrix is multiplied with its inverse which is unique. The inverse is not possible with just any kind of matrix, a matrix must be square and … Read more
The matrices can be multiplied to get product matrix and also they demonstrate all other mathematical properties. The power of matrices is another mathematical property of matrix where matrix is raised to a power using an exponent. This brings another question, does the exponent laws applies to matrices or not ? what type of matrices … Read more
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.Consistent SystemThe … 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 #1Let … 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 MatrixThe element in row and column of matrix becomes the row and column element in … 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 MultiplicationIf and are two matrices with sizes and respectively. The following conditions apply … 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 matrix … 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 NotationsAn augmented matrix is derived from the … 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 FormGiven an augmented matrix that … Read more
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