A matrix is a set of numbers that have been arranged in columns and rows, forming a rectangular array of numbers. These numbers are named as entries or elements of the matrix. English mathematician James Sylvester first introduced the term ‘Matrix’ in the 19th century. The algebraic aspect of matrices was developed by his friend Arthur Caley, who was the first one to apply the concept of matrices to study linear equations. The concept of matrices and inverse of matrix is still very useful in the study of linear equations.
Matrices are widely used in computer graphics where matrices are used to represent the transformation and rotation of images. If there are y rows and z columns the matrix is said to be the “y X z” matrix. A matrix with b rows and b columns is called a square matrix of order n. While when we multiply two ordinary numbers m and n, mn is always equal to nm, the same is not true for the multiplication of matrices as it is not commutative.
Another term associated with linear equations is ‘Inverse of Matrix’. The inverse of a matrix is a type of matrix that, when multiplied with the given matrix yields the multiplicative identity. This method is used to find solutions to linear equations using the matrix inversion method. The inverse of the matrix is possible if the value of the determinant of the matrix is non-zero. If the determinant of a given matrix has a non-zero value and the inverse matrix can be calculated, such a matrix is called an invertible matrix. Therefore, the inverse of the matrix can exist only if the given matrix is a square matrix and the determinant of the said matrix is not equal to zero.
Let us look at some important terms related to the inverse of a matrix. These terms will prove helpful in doing calculations related to the inverse of the matrix and will make the concept clearer.
Certain rules should be kept in mind while doing calculations about determinants:
If you want to go into further details, join one of the programs offered by Cuemath to get a clear understanding of the concept.
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