Performing row operations on a matrix is the method we use for solving a system of equations. In order to solve the system of equations, we want to convert the matrix to row-echelon form, in …

We may see the sequence in the leaf or branch arrangement, the number of petals of a flower, or the pattern of the chambers in a nautilus shell. Their growth follows the Fibonacci sequence, a …

Not all square matrices have an inverse, but if A A is invertible, then {A}^ {-1} A−1 is unique. We will look at two methods for finding the inverse of a 2\text {}\times \text {}2 2× 2 matrix and a …

Notice the change in notation. There are several ways to indicate the determinant, including [latex]\mathrm {det}\left (A\right) [/latex] and replacing the brackets in a matrix with straight …

Given the function f\left (x\right)=-3 {x}^ {2}\left (x - 1\right)\left (x+4\right) f (x) = −3x2 (x −1)(x +4), express the function as a polynomial in general form and determine the leading term, degree, …

Using algebra, we can verify that this shared point is actually \left (-3,-2\right) (−3,−2) and not \left (-2.999,-1.999\right) (−2.999,−1.999). By substituting the x x - and y y -values of the ordered …

Solving Quadratic Equations by Factoring An equation containing a second-degree polynomial is called a quadratic equation. For example, equations such as 2 {x}^ {2}+3x - 1=0 2x2 +3x −1 = …

If the slope is positive, the line slants to the right. If the slope is negative, the line slants to the left. As the slope increases, the line becomes steeper. Some examples are shown below. The …

Example Factor and solve the equation: {x}^ {2}+x - 6=0 x2 + x−6 = 0. Answer: To factor {x}^ {2}+x - 6=0 x2 +x −6 = 0, we look for two numbers whose product equals -6 −6 and whose sum …

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