Tag: Matrices and Determinants
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Adjoint of Matrix
Before studying this chapter, you will need to have a deep knowledge about: Minors and Co-factors in Matrix Adjoint of Matrix Let $\text{A = } [ a_{ij} ]_\text{mxn}$ be a matrix whose respective co-factors are $\text{C}_\text{ij}$. Then, the tranpose of co-factor matrix of a given matrix is defined as adjoint Matrix. Mathematically, Adjoint of matrix…
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Matrix Operations – Addition, Subtraction, and Multiplication
Mathematical operations like addition, subtraction and multiplication can be performed on matrices. However, one of the four fundamental operations – division of matrices is not defined. Addition of Matrices Let us consider two matrices $\text{A} = [ \text{a}_\text{ij}]_\text{mxn}$ and $\text{B} = [ \text{b}_\text{ij} ]_\text{mxn}$ having equal number of rows and columns $\text{(m = n)}$ then…
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Determinant of 3×3 Matrix
Determinant of a 3×3 Matrix is defined as the sum of products of each element and their respective cofactors, taking one row or one column at a time.
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Minors and Co-factors in Matrix
Before learning how to find the determinant of a 3×3 matrix, we must learn about what is minors and co-factors in matrix.
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Transpose of a Matrix
Transpose of a matrix is obtained by inter-changing the position of its rows and columns.
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Cramer’s Rule: Solution of a System of Linear Equations
Cramer’s Rule is used to solve the system of linear equations in two variables using determinants. Analytical Geometry and Cramer’s Rule Let us consider the following two linear equations: i) $a_1x + b_1y + c_1 = 0$ ii) $a_2x + b_2y + c_2 = 0$ The values of x and y which satisfy both the…
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Solution of a System of Linear Equations – Matrix Method
Introduction By notating the linear equations in matrix form and using the Inverse of Matrices, we can find the solution of the system of linear equations. Linear Equation: Any equation in the form of ax + by = c is called linear equation. Some examples of linear equations are: $6\text{x} + 5\text{y} = 1$ $9\text{x}…
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Inverse of 2×2 Matrix
Introduction If A be a square matrix of order mxm then the inverse matrix of A is another matrix of the order mxm, denoted by A-1 and defined as $\text{AA}^{-1} = \text{A}^{-1}\text{A} = \text{I}_m$ where $\text{I}m$ is a identity matrix of the same order as of the matrix A. In order to find out the…
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Determinant of 2×2 Matrix
Introduction In a 2×2 square matrix, the determinant is obtained by subtracting the product of the elements of the secondary diagonal by the product of the elements of the leading diagonal. Determinant of a matrix is written as |A| or |A+B| or |B|. The name of the the matrix should be written inside ‘||’. In…
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Types of Matrix
In the previous chapter, we discussed Introduction of Matrix. Here, we shall discuss Types of Matrix. Row Matrix Row Matrix is that type of matrix in which the entries are arranged in only one row and more than one columns. The general order of a row matrix is 1xn where n = 1,2,3,4,… . Examples…