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Problem 11

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology. HINT [See Examples 1-6.] $$ \begin{array}{r} x+y=0 \\ 3 x-y=1 \\ x-y=-1 \end{array} $$

Expert verified

The unique solution to the given system of equations using Gauss-Jordan row reduction is:
\[
\begin{array}{r}
x = 1 \\
y = -1 \\
z = 1
\end{array}
\]

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Chapter 2

Use technology to solve the systems of equations. Express all solutions as fractions. $$ \begin{array}{r} x+2 y-z+w=30 \\ 2 x-z+2 w=30 \\ x+3 y+3 z-4 w=2 \\ 2 x-9 y \quad+w=4 \end{array} $$

Chapter 2

Voting The U.S. Senate has 100 members. For a bill to pass with a supermajority, at least twice as many senators must vote in favor of the bill as vote against it. If all 100 senators vote in favor of or against a bill, how many must vote in favor for it to pass with a supermajority?

Chapter 2

Use technology to solve the systems of equations. Express all solutions as decimals, rounded to one decimal place. $$ \begin{aligned} &2.1 x+0.7 y-1.4 z=-2.3 \\ &3.5 x-4.2 y-4.9 z=3.3 \\ &1.1 x+2.2 y-3.3 z=-10.2 \end{aligned} $$

Chapter 2

Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. \(\begin{aligned} 100 x+4.5 y &=540 \\ 1.05 x+1.1 y &=0 \end{aligned}\)

Chapter 2

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology. HINT [See Examples 1-6.] $$ \begin{gathered} x+y-z=-2 \\ x-y-7 z=0 \\ \frac{2}{7} x \quad-\frac{8}{7} z=14 \end{gathered} $$

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