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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

Solving Simultaneous Equations by Matrix Inverse

Problem 2.5 # 37

Presented by E. G. Gascon

how to solve
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

finding a 1
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

alternate way to get a 1 using excel function minverse
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

solve for x matrix x a 1 b
Solve for X matrixX = A -1 B

=

Times

Use matrix multiplication or

MMULT function in Excel.

Ans: (15, -5, -1)