Performing Row Operations on a Matrix. Now that we can write systems of equations in augmented matrix form, we will examine the various row operations that can be performed on a matrix, such as addition, multiplication by a constant, and interchanging rows. Performing row operations on a matrix is the method we use for solving a system of equations.

Example: Showing That Matrix A Is the Multiplicative Inverse of Matrix B Show that the given matrices are multiplicative inverses of each other. [latex]A=\left[\begin ...

We eliminate one variable using row operations and solve for the other. Say that we wish to solve for [latex]x[/latex]. If equation (2) is multiplied by the opposite of the coefficient of [latex]y[/latex] in equation (1), equation (1) is multiplied by the coefficient of [latex]y[/latex] in equation (2), and we add the two equations, the variable [latex]y[/latex] will be eliminated.

Given the function [latex]f\left(x\right)=0.2\left(x - 2\right)\left(x+1\right)\left(x - 5\right)[/latex], express the function as a polynomial in general form and determine the leading term, degree, and end behavior of the function.

The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair [latex](4, 7)[/latex] is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations.

How To: Given a quadratic equation with the leading coefficient of 1, factor it. Find two numbers whose product equals c and whose sum equals b.; Use those numbers to write two factors of the form [latex]\left(x+k\right)\text{ or }\left(x-k\right)[/latex], where k is one of the numbers found in step 1.Use the numbers exactly as they are.

[latex]\begin{array}{ll}\tan \left(2\theta \right)=\frac{2\tan \theta }{1-{\tan }^{2}\theta }\hfill & \text{Double-angle formula}\hfill \\ \text{ }=\frac{2\tan \theta ...

Relating Angles and Their Functions When working with right triangles, the same rules apply regardless of the orientation of the triangle. In fact, we can evaluate the six trigonometric functions of either of the two acute angles in the triangle in Figure 5.

Solution Make sure mode is set to radians. To find [latex]\theta [/latex], use the inverse sine function. On most calculators, you will need to push the 2 ND button and then the SIN button to bring up the [latex]{\sin }^{-1}[/latex] function. What is …

Solving Absolute Value Inequalities As we know, the absolute value of a quantity is a positive number or zero. From the origin, a point located at [latex]\left(-x,0\right)[/latex] has an absolute value of [latex]x[/latex] as it is x units away.Consider absolute value as the distance from one point to another point.