💻 Solving Simulteneous

This lesson covers core applied mathematics concepts and their agricultural applications for BSc Agriculture learners.

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MATHS :: Lecture 21 :: Solving simulteneous equation and cramers rule

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INVERSE OF A MATRIX

Definition

Let A be any square matrix. If there exists another square matrix B Such that AB = BA = I (I is a unit matrix) then B is called the inverse of the matrix A and is denoted by A-1. The cofactor method is used to find the inverse of a matrix. Using matrices, the solutions of simultaneous equations are found.

Introduction to Vectors

Vector Transformations

Vector Dot Product and Vector Length

Unit Vectors

Matrix Vector Products

Matrices to solve a vector combination problem

Converting a line from Cartesian to vector form

Working Rule to find the inverse of the matrix Step 1: Find the determinant of the matrix. Step 2: If the value of the determinant is non zero proceed to find the inverse of the matrix. Step 3: Find the cofactor of each element and form the cofactor matrix. Step 4: The transpose of the cofactor matrix is the adjoint matrix. Step 5: The inverse of the matrix A-1 = Example Find the inverse of the matrix Solution Let A = Step 1 Step 2 The value of the determinant is non zero \A-1 exists. Step 3 Let Aij denote the cofactor of aij in Step 4 The matrix formed by cofactors of element of determinant is \adj A = Step 5 = __

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Summary Cheat Sheet

• Focus on core formulas, definitions, and solved patterns from this lesson.
• Practice stepwise derivations and numerical substitutions carefully.
• Connect each concept to practical agricultural problem-solving contexts.

References

1 source

Primary classroom notes and standard BSc Agriculture applied mathematics references.