SOLVE FOR THE CURRENT VALUE OF X , Y, Z. You may wish to verify in your electronic lab kit the actual current flowing in each loop.
Application of four simultaneous linear equations
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X +
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Y +
|
Z +
|
W
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= At Node A, KCL
|
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X +
|
Y +
|
Z +
|
W
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= At Node B, KCL
|
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4 X +
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2 Y +
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Z +
|
W
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= 8 Loop 1 , KVL |
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X +
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2 Y +
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5 Z +
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W
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= 9 Loop 2, KVL |
INITIAL CONDITION:
Answer, X = 1 A
detX =
Answer, Y = 2 A detY =
Answer, Z = 1 A detZ =
Answer, W = detW =
determinant 4 x 4 =
Validate your answer by substituting the value of X, Y, and Z in original equations.
You need to complete all the input box then NaN (Not a Number) error message will be fixed. Automatic computation
| 4 Ω value change to 7 ohms | 4 Ω Loop 1 |
| 2 Ω value change to 20 ohms | 2 Ω Loop 1 |
| 3 Ω value change to 6 ohms | 3 Ω Loop 2 |
| 2 Ω value change to 8 ohms | 2 Ω Loop 2 |
| 8 volts value change to 10 volts | 8 Volts original |
| V9 value UNCHANGE | 9 Volts original |
Reviewer on how to compute for determinant value of 4 x 4 Matrix.
Acquiring knowledge and skill on how to solve for determinant of 4 x 4 matrix is important in solving any four simultaneous linear equation. In the above example, determinant X ( detX), detY, detZ, and detW were computed. Then following Cramer's Rule, the solution for value of X, Y , Z, and W can be calculated. Doing this calculation by hand is very time consuming but thanks to computer and internet advancement, it is now possible to solve this problem in less than a minute using your smartphone. Now our brain can be used for higher level of thinking such as scenario analyis and decision making.
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