Determine the value of I1 in the set of equations used in this example.ExampleGiven that t...

Determine the value of I1 in the set of equations used in this example.

Example

Given that the coefficients are in ohms and the constants are in volts, determine the value of I2 from the following set of equations:

2I1 + 0.5I2 + 1I3 = 0

0.75I1 + 0I2 + 2I3 = 1.5

3I1+0.2I2 + 0I3 = −1

Evaluate the characteristic determinant as follows:

= [(2)(0)(0) + (0.5)(2)(3) + (1)(0.75)(0.2)] − [(3)(0)(1) + (0.2)(2)(2) + (0)(0.75)(0.5)]

= (0 + 3 + 0.15) − (0 + 0.8 + 0) = 3.15 − 0.8 = 2.35

Evaluate the determinant for I2 is as follows:

= [(2)(1.5)(0) + (0)(2)(3) + (1)(0.75)(−1)] − [(3)(1.5)(1)+ (−1)(2)(2) + (0)(0.75)(0)]

= [0 + 0 + (−0.75)] − [4.5 + (−4) + 0] = −0.75 − 0.5 = -1.25

Finally, divide the two determinants.

= −0.532 A = −532 mA