Transcription of 4.5 Solving Systems Using Inverse Matrices - …
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4.5 Solving Systems Using Inverse Matrices - …
Page 1 of 2230 Chapter 4 Matrices and DeterminantsSolving Systems Using Inverse MatricesSOLVINGSYSTEMSUSINGMATRICESIn Lesson you learned how to solve a system of linear equations Using Cramer srule. Here you will learn to solve a system Using Inverse the activity you learned that a linear system can be written as a matrix equation AX= B. The matrix Ais the coefficient matrix of the system , X is the andBis the Writing a Matrix EquationWrite the system of linear equations as a matrix equation. 3x+ 4y= 5 Equation 12x y = 10 Equation 2 SOLUTIONAX B = ..Once you have written a linear system as AX= B, you can solve for Xby multiplyingeach side of the matrix by A 1on the original matrix 1AX= A 1 BMultiply each side by A A 1BA 1A=IX= A 1 BIX=X5 10xy4 1 32 EXAMPLE 1matrix of of variables,GOAL1 Solve Systems oflinear equations usinginverse Systems oflinear equations to solvereal-lifeproblems, such asdetermining how muchmoney to invest in Example 4.
Page 1 of 2 4.5 Solving Systems Using Inverse Matrices 231 SOLUTION OF A LINEAR SYSTEM Let AX= Brepresent a system of linear equations. If the determinant of Ais nonzero, then the linear system has exactly one solution, which is X= Aº1B. Solving a Linear System Use matrices to solve the linear system in Example 1.
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