Cramer’s Rule is a simple rule that lets us use determinants to solve a system of equations. It tells us that we can solve for any variable in the system by calculating D_v/D, where D_v is the determinant of the coefficient matrix, with the answer column values substituted into the column representing the variable for which we’re trying to solve, and where D is the determinant of the coefficient matrix.
Read MoreWe know already how to solve systems of linear equations using substitution, elimination, and graphing. This time, we want to talk about how to solve systems using inverse matrices. To walk through this, let’s use a simple system.
Read MoreIn math and science you might meet a variable with a subscript. Don’t let them scare you, they’re just a way to keep track of variables that could be related to each other in some way. For instance, if we’re doing a problem involving the distance that two people travel, we might use the variables D_A and D_B to indicate the distances related to person A and person B, respectively.
Read MoreThroughout Linear Algebra, we’ll be really interested in solving systems of linear equations, or linear systems. A linear system is a system of equations, defined for a set of unknown variables, where each of the variables is linear (the variables are first degree, or raised to the power of 1).
Read MoreAge word problems are like number word problems. You’ll still need to relate sentences in English to mathematical equations to solve for people’s ages. In this lesson we’ll look at how to do that. One helpful way to organize these types of problems is by making a table.
Read MoreWe can solve a system of linear equations using the method of elimination. The elimination method has us eliminate one of the variables from the system in order to solve for the value of the other variable, and then turn around and use that value to find the value of the eliminated variable.
Read MoreTwo-step problems are problems in which you need to not only solve an equation for the value of a variable, but then also use the solution to evaluate some other expression that depends on that same variable.
Read MoreRemember that a solution to a system of equations is the set of numbers that makes all of the equations true. If a three variable system has a solution, it’ll have a solution for each of the three variables.
Read MoreThere are three ways to solve systems of linear equations: substitution, elimination, and graphing. Substitution will have you substitute one equation into the other; elimination will have you add or subtract the equations to eliminate a variable; graphing will have you sketch both curves to visually find the points of intersection.
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