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Solving Simultaneous Equations by Matrix Inverse

Solving Simultaneous Equations by Matrix Inverse. Problem 2.5 # 37 Presented by E. G. Gascon. The Problem. How to solve. To solve a system of equations AX = B, where A is the matrix of coefficients. B is the matrix of constants. Need to find A -1 the inverse of A.

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Solving Simultaneous Equations by Matrix Inverse

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  1. Solving Simultaneous Equations by Matrix Inverse Problem 2.5 # 37 Presented by E. G. Gascon

  2. The Problem

  3. How to solve To solve a system of equations AX = B, where A is the matrix of coefficients. B is the matrix of constants. Need to find A-1 the inverse of A So… solving for X = A -1 B

  4. Finding A-1 Start by setting up the matrix with the identity in the last three columns After performing Gauss-Jordan, the resulting matrix is A-1 See next slide for Gauss- Jordan Work

  5. Gauss –Jordan to find A-1

  6. Alternate way to get A-1 using Excel Function MINVERSE Step 1: Enter the 3X3 coefficient matrix in an Excel Spread Sheet. Step 2: Select a 3X3 matrix of empty cells and type =MINVERSE( matrix is step 1) Ctrl + Shift + ENTER

  7. Solve for X matrixX = A -1 B = Times Use matrix multiplication or MMULT function in Excel. Ans: (15, -5, -1)

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