One of the most common applications of square matrices is to solve systems of linear equations. Solving linear systems using matrix algebra is more efficient than hand calculating the systems using substitution methods; this is especially true when dealing with systems of 3 or more variables. Two matrix algebra methods include: row reducing and finding the inverse.

How Do You Solve Linear Systems Using Matrix Algebra?

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• Systems of Linear Equations and Matrices
• Inverse of a square matrix
• The Identity Matrix

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When simplifying square roots, we give the positive and negative answer if solving an equation that did not originally have a square root. Otherwise, we give only the principal root. Square roots of negative numbers have non-real answers, which is why square roots of variables sometimes include the condition that the variable is greater than zero. Knowledge of math radicals is important when solving quadratic equation problems.

How do you simplify radicals?

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• Solving Radical Equations
  
• Adding and Subtracting Radical Expressions
• Multiplying and Distributing Radical Expressions
• Estimating Square Roots

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It takes practice and a few useful methods to decide where to start when solving equations with a variable on both sides of the equals sign. There are many methods we use to solve for the variable when it appears in more than one place. You need to know how to combine like terms, as well as the skills needed to solved multi-step equations.

How Do You Solve Equations with Variables on Both Sides

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When you are given a trinomial, or a quadratic equation, it can be useful to factor the equation for the purposes of canceling and simplifying. Factoring trinomials is easiest when the leading coefficient (the coefficient on the squared term) is one. A more complex situation is factoring trinomials when the leading coefficient is not one. To factor trinomials we use methods that involve finding the factors of their coefficients.

How Do You Factor Trinomials, where A=1?

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When you simplifying complex fractions, factor the numerator and denominator into terms multiplying each other and look for equivalents of one (something divided by itself). Include parenthesis around any expression with a “+” or “-” and if all terms cancel in the numerator, there is still a one (1) there.

How Do You Simplify Complex Fractions?

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• Definition and Domain of a Rational Expression
• Solving a Rational Equation
• Multiplying and Dividing Rational Expressions

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To solve a system of linear equations, we can use substitution, elimination or something we call augmented matrices. To use matrices to solve a system of linear equations, we first enter the values associated with each of the variables and the answer. Once we put the information into a matrix (a rectangular array of numbers), we can use matrix operations to solve the equation.

Example of an Augmented Matrix

augmented matrix

Definitions:

• Elements: Each of the entries in the augmented matrix
• Rows: The numbers or variables that run across the matrix.
• Columns: The numbers or variables that run down the matrix.
• The diagonal of the matrix: The set of elements that starts at the top, left corner and runs diagonally down and to the right. (This diagonal: 2, -1 and 4.)

What Is An Augmented Matrix?

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Solving quadratics can be difficult. Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by factoring, using the square roots, or using the quadratic formula. The cool thing is that solving quadratic equations by completing the square will always work when solving quadratic equations, and the technique is a good tool to have in your math tool belt.

How Do You Complete the Square?

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• The Vocabulary of Quadratic Polynomials
• How Do You Solve Quadratic Equations with Factoring?
• How Do You Solve Quadratic Equations Using Square Roots?
• How Do You Derive The Quadratic Formula?a=6001040″ target=”_blank”

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We use the identity matrix to calculate a the inverse of a square matrix. In order to be invertible, a matrix must be square. By finding the square matrix inverse, we can find the solution of a system of linear equations. A square matrix inverse, when multiplied on the left or right by the original matrix gives us the identity matrix.

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• Systems of Linear Equations and Matrices
• How Do You Solve Linear Systems Using Matrix Algebra?
• The Identity Matrix

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A variable is a symbol, such as x, that is used to describe an unknown number. In functions variables often represent not one number, but many different numbers. Understanding variables is essential for you to understanding problems that will need to be graphed.

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• What Are Additive and Multiplicative Inverses?
• How Do You Simplify Expressions and Combine Like Terms?

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Graphing Lines Using a Table of Values

We often use a table of values to plot and connect points when we are graphing a line. Sometimes graphing lines using an equation involves the same methods as using a table of values. There are several other methods of graphing lines, including using the point-slope method. Understanding how graphs, tables and equations all work in harmony is essential to your understanding of Algebra.

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• Linear Equations and Their Graphs
• How Do You Graph Lines using Intercepts
• How Do You Create the Point-Slope Form of Linear Equations

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