Example of Finding a System of Linear Equations from an Augmented Matrix
Example of Finding a System of Linear Equations from an Augmented Matrix

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3.6 Solving Systems Using Matrices You can use a matrix to represent and solve a system of equations without writing the variables. A matrix is a rectangular array of numbers. You usually display the array within brackets. The dimensions of a matrix are the numbers of rows and columns in the array.

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Matrices Each number in a matrix is a matrix element. You can identify a matrix element by its row and column numbers. – In matrix A, a 12 is the element in row 1 and in column 2. – So, a 12 is the element 4.

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Representing Systems with Matrices How can you represent the system of equations with a matrix? 2x + y = 9 x – 6y = -1

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Representing Systems with Matrices How can you represent the system of equations with a matrix? x – 3y + z = 6 x + 3z = 12 y = -5x + 1 5x + y = 1

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Writing a System from a Matrix What linear system of equations does this matrix represent? 5x + 2y = 7 0x + 1y = 9 5x + 2y = 7 y = 9

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Row Operation You can use a matrix that represents a system of equations to solve the system. Your goal is to use row operations to get a matrix in the form or Notice that the first matrix represents the system x = a, y = b, which then will be the solution of a system of two equations in two unknowns. The second matrix represents the system x = a, y = b, and z = c.

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Solving a System Using a Matrix What is the solution of the system? x + 4y = -1 2x + 5y = 4 See solution on p. 177, example 4.

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Using a Calculator to Solve a Linear System See example 5 on p. 178.

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More Practice!!!!! Homework – Textbook p. 179 – 180 #8 – 29.

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