4.4.H: Homework

1. \(\left\{ \begin{array} {l} -3x+y+z=-4 \\ -x+2y-2z=1 \\ 2x-y-z=-1 \end{array} \right. \)

ⓐ \((−5,−7,4)\)
ⓑ \((5,7,4)\)

Answer

ⓐ no ⓑ yes

2. \(\left\{ \begin{array} {l} 6x−5y+2z=3 \\ 2x+y−4z=5 \\ 3x−3y+z=−1 \end{array} \right. \)

Answer

\((4,5,2)\)

3. \(\left\{ \begin{array} {l} 5x−3y+2z=−5 \\ 2x−y−z=4 \\ 3x−2y+2z=−7 \end{array} \right. \)

Answer

\((7,12,−2)\)

4. \(\left\{ \begin{array} {l} 4x−3y+z=7 \\ 2x−5y−4z=3 \\ 3x−2y−2z=−7 \end{array} \right. \)

Answer

\((−3,−5,4)\)

5. \(\left\{ \begin{array} {l} x−2y+2z=1 \\ −2x+y−z=2 \\ x−y+z=5 \end{array} \right. \)

Answer

no solution

30. Kirchhoff’s Current Law states that the total current flowing into any junction (or node) in a circuit must equal the total current flowing out of it. In other words, the sum of all currents entering and leaving any point is zero.

Kirchhoff’s Voltage Law states that the sum of the voltage changes around any closed loop in a circuit is zero. In other words, the total voltage gains and drops around a complete loop must balance.

Applying Kirchhoff’s laws of current and voltage to node B in the circuit shown below yields the following equations:

\(\left\{ \begin{array} {l} I_1+I_2−I_3=0 \\ 5I_1−4I_2−7=0 \\ 4I_2+I_3−13=0 \end{array} \right. \)

Find the currents associated with \(I_1\), \(I_2\) and \(I_3\).

Answer

\(I_1=3\) A, \(I_2=2\) A, \(I_3=5\) A (Current is measured in amperes, amps for short, and symbolized using A.)