Answer to Question #293436 in Linear Algebra for abeni

Question

Define the following terms

PART 1.

a) What is an equation?

b) What is a linear equation?

c) What is determinants?

d) What is a matrix?

e) What is linear programming?

Answer 1

(a). An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression.

(b). Linear equations are the equations of degree 1. It is the equation for the straight line.

(c). A determinant can be defined in many ways for a square matrix.

The first and most simple way is to formulate the determinant by taking into account the top row elements and the corresponding minors. Take the first element of the top row and multiply it by it’s minor, then subtract the product of the second element and its minor. Continue to alternately add and subtract the product of each element of the top row with its respective minor until all the elements of the top row have been considered.

(d). Matrices are the ordered rectangular array of numbers, which are used to express linear equations. A matrix has rows and columns. we can also perform the mathematical operations on matrices such as addition, subtraction, multiplication of matrix. Suppose the number of rows is m and columns is n, then the matrix is represented as m × n matrix.

(e). Linear programming (LP) or Linear Optimisation may be defined as the problem of maximizing or minimizing a linear function that is subjected to linear constraints. The constraints may be equalities or inequalities. The optimisation problems involve the calculation of profit and loss.  Linear programming problems are an important class of optimisation problems, that helps to find the feasible region and optimise the solution in order to have the highest or lowest value of the function.