Chapter 4 Review

Chapter 4 Review - Use elementary row operations to...

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Chapter 4 Review A system of linear equations consists of two or more linear equations. A solution of a system of two equations in two variables is an ordered pair (x, y) that makes both equations true. This solution is the point where the graphs intersect. Methods of solving a system of equations: Graphing – graph both lines and find the point where they intersect. Substitution – solve one equation for a variable, substitute the resulting expression into the other equation, and solve for the other variable. Elimination/Addition – Put both equations in standard form and add them together. You may have to multiply one or both equations by a number so that one variable is eliminated when the equations are added. Matrices - Write a matrix to represent the system of equations.
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Unformatted text preview: Use elementary row operations to transform the matrix into an equivalent matrix with ones along the diagonal and zeros below the diagonal. Elementary row operations: 1. Interchange any two rows 2. Multiply (or divide) the elements of one row by the same nonzero number. 3. Multiply (or divide) the elements of one row by the same nonzero number and add to its corresponding elements in any other row. Cramers Rule: Find D, D x , D y , and D z (if applicable) x = D x / D y = D y / D z = D z / D If D=0 you must use another method to determine whether there is no solution or an infinite number of solutions. Determinants: The determinant of a 2x2 matrix abcd = ad - bc...
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Chapter 4 Review - Use elementary row operations to...

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