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Use’s Excel Array Formulas to Solve Simultaneous Equations

Use’s Excel Array Formulas to Solve Simultaneous Equations. Simultaneous Linear Equation. Present Example. The example we will consider here is from resistor circuits and goes by the name Kirchhoff’s circuit laws. The variables are currents in different “loops” of the circuit.

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Use’s Excel Array Formulas to Solve Simultaneous Equations

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  1. Use’s Excel Array Formulas to Solve Simultaneous Equations

  2. Simultaneous Linear Equation

  3. Present Example • The example we will consider here is from resistor circuits and goes by the name Kirchhoff’s circuit laws. • The variables are currents in different “loops” of the circuit. • The coefficients (numbers multiplying the variables) are resistances. • The constants are voltages.

  4. Example with numbers • 5 = 3.2 JA – 1.0 JB - 2.2 JC • 0 = -1.0 JA + 5.5 JB – 3.0 JC • 0 = -2.2 JA – 3.0 JB + 6.9 JC • In the above we have three current variables: JA, JB and JC.

  5. Loop equations as matrix equation • 5 = 3.2 JA – 1 JB - 2.2 JC • 0 = -1 JA + 5.5 JB – 3 JC • 0 = -2.2JA – 3 JB + 6.9 JC

  6. Enter matrix in Excel, highlight a region the same size as the matrix.

  7. In the formula bar, enter =MINVERSE(range) where range is the set of cells corresponding to the matrix (e.g. B1:D3). Then hit Crtl+Shift+Enter

  8. Result of matrix inversion

  9. Prepare the “voltage vector”, then highlight a range the same size as the vector and enter =MMULT(range1,range2) where range1 is the inverse matrix and range2 is the voltage vector. Then Ctrl-Shift-Enter. Voltage vector

  10. Results of Matrix Multiplication

  11. The answer • The current vector is the answer • JA=3.152 mA • JB=1.470 mA • JC=1.644 mA

  12. Use the matrix approach in Excel to find the solution for • 10 = 7 JA – 3 JB - 4 JC • 0 = -3 JA + 6 JB – 1 JC • 0 = -4 JA – 1 JB + 10JC

  13. Atomic Isotope Problem • Atomic MassesIsotopes:The element indium exists naturally as two isotopes. 113In has a mass of 112.9043 amu, and 115In has a mass of 114.9041 amu. The average atomic mass of indium is 114.82 amu. Calculate the percent relative abundance of the two isotopes of indium. • http://eppe.tripod.com/stoictry.htm

  14. Use the matrix approach in Excel to find the solution for • 112.9043 x + 114.9041 y = 114.82x + y = 1 where x is the fraction of the first isotope and x is the fraction of the second isotope.

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