linear dependence and independence

The process of finding the value of the unknown quantity for which the equation is true, is called solving the equation. The value so found is called the root or solution of the equation.The process of finding the value of the unknown quantity for which the equation is true, is called solving the e..

Select the requirements of a binomial probability experiment. I. There must be fixed number of trials. II. Each trial can have only two outcomes, or outcomes that can be reduced to two outcomes. III. The outcomes of each trial must be dependent on each other. IV. The outcomes of each tria..

ax + b = 0 is a linear equation in one variable. Consider the equation 2x + 4 = 0 2x = -4 x = -2 Since this equation is independent of y, for all values of y, x = -2 Hence x = -2 is a line parallel to the y-axis at x = -2. Consider the equation y - 5 = 0 y - 5 = 0 y = 5 Since th..

Which of the following statement(s) is/are true? I. If the correlation coefficient is significant, the equation of the regression line cannot be determined. II. The values of the dependent variable can be predicted for the values of the independent variable using the regression ..

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..

Solve the system of equations. Determine whether the system is consistent and independent, consistent and dependent, or inconsistent by using augmented matrices. x + 4 y = 8 4 x + 16 y = 5 => (- 8, - 27); consistent and dependent or (8, - 27); consistent and indep..

Solve the system of equations. 3 x + 4 y = 8 x - 6 y = 10 Determine whether the system is consistent and independent, consistent and dependent, or inconsistent by using augmented matrices. => (4, - 1); consistent and independent or (0, 0); inconsistent or (4, 1); consi..

The table shows the performance of 500 students in mathematics and physics. At α = 0.05, find the chi-square test value and test the hypothesis that the performance in physics is independent of the performance in mathematics. => 272.2, the performance in physics is in some way ..

Determine whether the system is consistent and independent, consistent and dependent, or inconsistent by using augmented matrices. 2 x - y + z = 10 x + y + z = 5 3 x + 2 z = 15 => consistent and dependent or consistent and independent or inconsistent..

State whether the system is consistent and independent, consistent and dependent or inconsistent using the elimination method. 9 x + y = 10 y - 9 z = 82 10 x + 10 z = - 80 => Inconsistent or Cannot be determined or Consistent and dependent or Consistent and indepe..