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Solving Systems of Linear Equations Using Matrix and Solver Methods

This guide explores how to solve systems of linear equations using matrix and solver methods in spreadsheets. To use the matrix method, enter coefficients and constants, then calculate the inverse and multiply for solutions. This method allows for quick recalculations if coefficients change. However, it cannot be used for non-linear equations. The solver method can solve non-linear equations but may require tedious initial guesses and frequent reruns for any problems changes. Also included is a practical example of temperature distribution across a square plate.

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Solving Systems of Linear Equations Using Matrix and Solver Methods

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  1. Solving Systems of Linear Equations

  2. Enter the Coefficients and Constants from the Equations

  3. In an empty cell, type =minverse(data range), Enter

  4. Select a range that is the same size as the coefficient matrix

  5. Press F2, then Ctrl+Shift+Enter

  6. In a blank cell, type =mmult(range1,range2), Enter

  7. Select a range containing the first cell that contains the same number of cells as unknowns

  8. Press F2, Ctrl+Shift+Enter

  9. Benefits of Matrix Method • Coefficients and Constants can be changed and the solutions are immediately calculated • Applies easily to large systems of equations. • Shortfalls: • Cannot be used for non-linear equations

  10. Benefits of Solver Method • Can be used for all non-linear equations • Shortfalls: • Tedious for large systems of equations. • Initial guesses must be given, and solution may not converge if the guesses are not close to the actual solution. • Any change in the problem requires that Solver be rerun again.

  11. Temperature Distribution in a Square Plate 100 oC 50 oC 75 oC 25 oC

  12. j i Solution

  13. 100 oC T11 T12 T13 T21 T22 T23 50 oC 75 oC T31 T33 T32 25 oC

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