Solving Systems of Linear Equations

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Solving Systems of Linear Equations
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Enter the Coefficients and Constants from the
Equations
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In an empty cell, type minverse(data range),
Enter
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Select a range that is the same size as the
coefficient matrix
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Press F2, then CtrlShiftEnter
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In a blank cell, type mmult(range1,range2), Enter
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Select a range containing the first cell that
contains the same number of cells as unknowns
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Press F2, CtrlShiftEnter
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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

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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.

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Temperature Distribution in a Square Plate
100 oC
50 oC
75 oC
25 oC
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Solution
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100 oC
T11
T12
T13
T21
T22
T23
50 oC
75 oC
T32
T33
T31
T11 T12 T13 T21 T22 T23 T31 T32 T33 Constant
-4 1 1 -175
1 -4 1 1 -100
1 -4 1 -150
1 -4 1 1 -75
1 1 -4 1 1 0
1 1 -4 1 -50
1 -4 1 -100
1 1 -4 1 -25
1 1 -4 -75
25 oC