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Chapter 8: Problem 5
Find the determinant of the matrix. $$[4]$$
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Consider the circuit in the figure. The currents \(I_{1}, I_{2},\) and \(I_{3},\) in amperes, are given by the solution of the system of linear equations \(\left\\{\begin{aligned} 2 I_{1} &+4 I_{3}=E_{1} \\ I_{2}+4 I_{3} &=E_{2} \\\ I_{1}+I_{2}-I_{3} &=0 \end{aligned}\right.\) where \(E_{1}\) and \(E_{2}\) are voltages. Use the inverse of the coefficient matrix of this system to find the unknown currents for the given voltages. \(E_{1}=10\) volts, \(E_{2}=10\) volts
Use matrices to solve the system of equations, if possible. Use Gaussian elimination with back-substitution. $$\left\\{\begin{array}{l} -x+y=-22 \\ 3 x+4 y=4 \\ 4 x-8 y=32 \end{array}\right.$$
Consider the system of equations. $$\left\\{\begin{array}{l} y=b^{x} \\ y=x^{b} \end{array}\right.$$ (a) Use a graphing utility to graph the system of equations for \(b=2\) and \(b=4\) (b) For a fixed value of \(b > 1,\) make a conjecture about the number of points of intersection of the graphs in part (a).
Solve for \(x\) $$\left|\begin{array}{cc} 2 x & -3 \\ -2 & 2 x \end{array}\right|=3$$
Find the domain of the function and identify any horizontal or vertical asymptotes. $$f(x)=\frac{x^{2}+2}{x^{2}-16}$$
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