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Mathematics

inverse matrix method

Subject: 
Algebra
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inverse matrix

Inverse Matrix Method The inverse matrix method is a method of solving an unsolved system of equations by using a matrix and the formula AA=I and AX= B to find the solution to the variables where I is the identity matrix. Start with your unsolved linear system. You must make sure that you have an equal number of variables and equations or the method won?t work. Line the coefficients up in a matrix by system. For example, If your systems were: -1x + 1y + 3z = 2 -1 1 3 x 2 2 x + 1y +2z = 2 then you would arrange it as 2 1 2 y 2

Basic Algebraic Laws

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Algebra
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Commutative property
Commutative Law For Addition: -------------------------------------------------------------------------------- a + b = b + a ex. 5 + 7 = 7 + 5 =12 -------------------------------------------------------------------------------- Commutative Law For Multiplication: -------------------------------------------------------------------------------- a x b = b x a ex. 3 x 6 = 6 x 3 = 18 -------------------------------------------------------------------------------- Associative Law For Addition: -------------------------------------------------------------------------------- (a + b) + c = a + (b + c) ex. (4 + 6) + 5 = 4 + (6 + 5) = 15 -------------------------------------------------------------------------------- Associative Law For Multiplication:

Slope-intercept Form

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Algebra
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Slope
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Common exercises will give you some pieces of information about a line, and you will have to come up with the equation of the line. How do you do that? You plug in whatever they give you, and solve for whatever you need, like this: Find the equation of the straight line that has slope m = 4 and passes through the point (?1, ?6). Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line, they have given me an x-value and a y-value for this line: x = ?1 and y = ?6.

Definition and Domain of Rational Functions

Subject: 
Calculus
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Definition and Domain of Rational Functions A rational function is defined as the quotient of two polynomial functions. f(x) = P(x) / Q(x) Here are some examples of rational functions: g(x) = (x2 + 1) / (x - 1) h(x) = (2x + 1) / (x + 3) The rational functions to explored in this tutorial are of the form f(x) = (ax+b)/(cx + d) where a, b, c and d are parameters that may be changed, using sliders, to understand their effects on the properties of the graphs of rational functions defined above. Example: Find the domain of each function given below. g(x) = (x - 1) / (x - 2) h(x) = (x + 2) / x Solution

Add+Subtract Rational Expressions

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Algebra
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Homework ???????????????Grade?8 Name:?___________________________________________ Date:?__________ The?LCM?of?two?rational?algebraic?expressions?is?often?used?to?add?or?subtract?the?two? expressions.?The?method?used?is?to?identify?all?common?factors?in?the?denominator?of? the?expressions,?and?multiply?the?numerators?by?the?uncommon?factors?(exactly?like?you? would?for?non?algebraic?fractions).? Add?or?subtract?the?following?expressions,?by?first?finding?the?LCD. 1. ????a???+????????a?+?x??????+???ax????? ???????????x???a?????x2?+?ax?+?a2??????x3???a3 2. ??1?????+??????5?????+???? ??x? ??????? ?? ???????????x?+?1????4x?+?4????x2???1 ?? 3. ????1?????+?????2x??????+???3x????+????x??????? ??????????3x???3??????(x???1)2???x?+?1?????(x?+?1)2?

Quadratic Formula

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Algebra
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Equations
Quadratic forms
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Quadratic
Factoring
Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution. The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients". The Formula is derived from the process of completing the square, and is formally stated as: For ax2 + bx + c = 0, the value of x is given by:

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