06Solving Linear Systems

# 06Solving Linear - 5 17 1 1 y x-= 5 14 5 17 y x Ex Find the solution to the system 11 4 2 2 4-=-= y x y x Ex Find the solution to the linear system

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S OLVING L INEAR S YSTEMS As you saw in grade 11, matrices can be used to solve linear systems of equations. Ex . Represent the system of equations in matrix form. 1 4 3 4 2 - = + = + y x y x - = 1 4 4 3 1 2 y x If the first two matrices are multiplied, you get: - = + + 1 4 4 3 2 y x y x The top elements must be equal and the bottom elements must be equal. To find the solution, pre-multiply each matrix by the inverse of the 2 x 2 matrix. The inverse is - - 5 2 5 3 5 1 5 4 . - × - - = × × - - 1 4 5 2 5 3 5 1 5 4 4 3 1 2 5 2 5 3 5 1 5 4 y x Remember that multiplying a matrix and its inverse results in the identity matrix. - = × 5 14

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Unformatted text preview: 5 17 1 1 y x -= 5 14 5 17 y x Ex . Find the solution to the system: 11 4 2 2 4-=--= + y x y x . Ex . Find the solution to the linear system of three equations. The method is the same. 1 3 9 7 3 2-=--= + + =--z y x z y x z y x Find the inverse of the three by three matrix. To use the GDC, enter the coefficient matrix into [A], enter the right hand side into [B]. Then multiply B A ×-1 to obtain the solution. Ex . Use the GDC to find the solution to the system below. 540 5 2 4 460 3 4 2 150 = + + = + + = + + z y x z y x z y x Assign: MM Exercise 27.5 #1 manual evens, GDC odds, 4...
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## This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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06Solving Linear - 5 17 1 1 y x-= 5 14 5 17 y x Ex Find the solution to the system 11 4 2 2 4-=-= y x y x Ex Find the solution to the linear system

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