<jupyter_start><jupyter_text>Members:<NAME> © 2021<NAME> © 2021<NAME> © 2021<NAME> © 2021  Problem: The currents running through an electrical system are given by the following system of equations.  The three currents, I1, I2, and I3, are measured in amps.  Solve the system to find the currents in this circuit. [[1](http://www.algebralab.org/practice/practice.aspx?file=Word_ApplicationProblemFor3EquationsWith3Variables.xml)]$$I_1 + 2I_2 - I_3 = 0.425 \\3I_1 - I_2 + 2I_3 = 2.225\\5I_1 + I_2 + 2I_3 = 3.775\\$$ Standard Bracketed Form:$$ \left\{    \begin{array}\\        I_1 + 2I_2 - I_3 = 0.425 \\        3I_1 - I_2 + 2I_3 = 2.225\\        5I_1 + I_2 + 2I_3 = 3.775\\    \end{array}\right.$$Linear Combination Form (Matrix):$$\begin{bmatrix}1&2&-1\\3&-1&2\\5&1&2\end{bmatrix} \cdot \begin{bmatrix}I_1\\I_2\\I_3\end{bmatrix} = \begin{bmatrix}0.425\\2.225\\3.775\end{bmatrix}$$  Programmed Algorithm:<jupyter_code>import numpy as np
import matplotlib.pyplot as plt  
X = np.array([
    [1,2,-1],
    [3,-1,2],
    [5,1,2]
])
Y = np.array([
    [0.425],
    [2.225],
    [3.775]
])
currents = np.linalg.solve(X, Y)
for i in range(currents.size):
    print(f'I{i+1} = {round(float(currents[i]),2)} A')<jupyter_output>I1 = 0.37 A
I2 = 0.4 A
I3 = 0.75 A<jupyter_text>Vector Visualization:<jupyter_code>plt.figure(figsize=(5,5)) 
plt.plot(currents, 'o-')
plt.title('Vector Visualization')
plt.ylabel('Current')
plt.tick_params(bottom=False,
                labelbottom=False)
plt.ylim(0.35,0.8)
plt.grid()
plt.show()<jupyter_output><empty_output>
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