Solving System of Simultaneous Equations in Mathcad: Three Methods, Assignments of Microelectronic Circuits

This document demonstrates how to solve a system of simultaneous equations using three different methods in mathcad: determinants, matrix inversion, and a solve block. The given system of equations is 2x - 1y + 1z = 2, 1x + 1y - 2z = 7, and 2x + 3y + 1z = -2.

Typology: Assignments

Pre 2010

Uploaded on 08/03/2009

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Solving a system of simultaneous equations in Mathcad utilizing determinants :
Given Information:
2x - 1y + 1z = 2
1x + 1y - 2z = 7
2x + 3y + 1z = -2
Mathcad definitions and solutions:
x
2
7
2
1
1
3
1
2
1
2
1
2
1
1
3
1
2
1
y
2
1
2
2
7
2
1
2
1
2
1
2
1
1
3
1
2
1
z
2
1
2
1
1
3
2
7
2
2
1
2
1
1
3
1
2
1
=x2=y1=z3
Solving a system of simultaneous equations in Mathcad utilizing matrix inversion :
Given Information:
2x - 1y + 1z = 2
1x + 1y - 2z = 7
2x + 3y + 1z = -2
Mathcad definitions and solutions:
A
2
1
2
1
1
3
1
2
1
B
2
7
2
C.
A1B
xC0yC1zC2
=C
2
1
3=x2=y1=z3
pf2

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Solving a system of simultaneous equations in Mathcad utilizing determinants : Given Information: 2x - 1y + 1z = 2 1x + 1y - 2z = 7 2x + 3y + 1z = -

Mathcad definitions and solutions:

x

y

z

x = 2 y = 1 z = 3

Solving a system of simultaneous equations in Mathcad utilizing matrix inversion :

Given Information:

2x - 1y + 1z = 2 1x + 1y - 2z = 7 2x + 3y + 1z = -

Mathcad definitions and solutions:

A

B

C A 1.^ B

x C 0 y C 1 z C 2 C =

3 x^ =^2 y^ =^1 z^ =^3

Solving a system of simultaneous equations in Mathcad utilizing a solve block :

Given Information: 2x - 1y + 1z = 2 1x + 1y - 2z = 7 2x + 3y + 1z = -

Mathcad definitions and solutions:

x 1 y 1 z 1 (these are the initial guesses for the 3 unknowns) Given 2 x. 1 y. 1 z. 2 (note that constrained equality , Ctrl = , is used in the 3 equations ) 1 x^. 1 y. 2 z. 7 2 x. 3 y. 1 z. 2

x y z

Find( x y z, , ) x = 2 y = 1 z = 3