by Kardi Teknomo

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Solving Linear Equation using Excel

This tutorial will describe how to use an inverse function for matrix in Microsoft Excel to solve non-homogeneous simultaneous linear equations.

The spreadsheet example can be downloaded here .

Suppose we want to solve simultaneous equations below

Solving linear equation

We can convert the simultaneous equations above into matrix form Solving linear equation where

Solving linear equation , Solving linear equation and Solving linear equation

The solution of the simultaneous equations can be easily obtained using inverse matrix

Solving linear equation

Solving linear equation

solution linear equation

Here is systematically how to do it in Microsoft Excel.

You may download the spreadsheet example here .

  1. Input the numbers of matrix Solving linear equation and vector Solving linear equation
  2. Tell MS Excel the name of this matrix by menu Insert-Name-Define . Solving linear equation

3. A defined-name dialog will appear and type the name of matrix Solving linear equation and refer to the range of the matrix Solving linear equation , then click OK. In a similar way, you define the name of vector Solving linear equation .

Solving linear equation

4. In a cell where do you want to put the inverse of matrix Solving linear equation , you type =MINVERSE( Solving linear equation ) . It will give you only one number. Now using the mouse highlight the range where do you want to put the inverse of matrix Solving linear equation . Because you know that the size of inverse Solving linear equation is also 3 by 3 matrix, highlight only that range. Solving linear equation While highlighting, press F2 and then Shift-Ctrl-Enter. You will get the inverse of matrix Solving linear equation .

5. Now you define name of inverse matrix and use matrix multiplication function to get the solution. To do that, in the cell where do you want to put the solution, type =MMULT(Inverse_A,b). It will give you only one number. Now using the mouse highlight the range where do you want to put the solution. Because you know that the size of solution is a single column with 3 rows, highlight only that range. While highlighting, press F2 and then Shift-Ctrl-Enter and you will get the solution.

Solving linear equation

See also:
MS Excel Tutorial index , Kardi Teknomo's Tutorial , Online interactive program to solve simulateneous equations using generalized inverse

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