what is a dependent variable in mathematics

We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..

We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan method e..

Each circular permutation corresponds to n linear permutations depending on where we start. Since there are exactly n! linear permutations, there are exactly permutations. Hence, the number of circular permutations is the same as (n-1)..

The above discussion leads to find the solution of a system of linear equations in two variables by using Cramer's rule. Cramer's rule suggests the use of determinants to solve a system of linear equations. Let us denote a 1 b 2 - a 2 b 1 (Denominators of x and y in (4) and (5)) as the de..

Consider an example. A person was asked to measure the thickness of a coin. He recorded the following readings: (i) 0.2 cm with ruler (ii) 0.23 cm with vernier (iii) 0.231 cm with micrometer The accuracy of thickness of the coin depended on the instrument used for measuring the thickness..

Which of the following statement(s) is/are true? I. The variable that cannot be controlled or manipulated is dependent variable. II. Independent variable is plotted on the y-axis. III. A relationship between four variables only is called multiple re..

For any specific value of the independent variable, the values of the dependent variable y are normally distributed. This is called the __________ assumption. => independence or linearity or equal - variance or normality..

A function is described by the equation f ( x ) = 2 x + 1. The replacement set for the independent variable is {0, 2, 3, 4}. Which of the following is contained in the corresponding set for the dependent variable? => 9 or 2 or 3 or 15..

A function is described by the equation f ( x ) = 3 x + 5. The replacement set for the independent variable is {1, 2, 5, - 7}. Which of the following is contained in the corresponding set for the dependent variable? => - 1 or - 16 or 26 or - 8..

Which of the following statement(s) is/are true? I. A multiple regression equation with three independent variables x 1 , x 2 and x 3 and one dependent variable would have the form y′ = a + b 1 x 1 + b 2 x 2 + b 3 x 3 . II. A multiple regression equation with two..