Chapter 6: Problem 44
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Models for controlling traffic flow are based on an equal number of cars entering an intersection and leaving that intersection.
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Chapter 6: Problem 44
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Models for controlling traffic flow are based on an equal number of cars entering an intersection and leaving that intersection.
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Write each system in the form \(A X=B\). Then solve the system by entering \(A\) and \(B\) into your graphing utility and computing \(A^{-1} B\). $$\left\\{\begin{array}{c}x-y \quad=1 \\\6 x+y+20 z=14 \\\y+3 z=1\end{array}\right.$$
Determinants are used to show that three points lie on the same line (are collinear). If $$\left|\begin{array}{lll}x_{1} & y_{1} & 1 \\\x_{2} & y_{2} & 1 \\\x_{3} & y_{3} & 1\end{array}\right|=0$$ then the points \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\) and \(\left(x_{3}, y_{3}\right)\) are collinear. If the determinant does not equal 0 , then the points are not collinear. Are the points \((-4,-6),(1,0),\) and \((11,12)\) collinear?
In Exercises \(37-44\), perform the indicated matrix operations given that \(A, B,\) and \(C\) are defined as follows If an operation is not defined, state the reason. $$A=\left[\begin{array}{rr}4 & 0 \\\\-3 & 5 \\\0 & 1\end{array}\right] \quad B=\left[\begin{array}{rr} 5 & 1 \\\\-2 & -2\end{array}\right] \quad C=\left[\begin{array}{rr}1 & -1 \\\\-1 & 1\end{array}\right]$$ $$B C+C B$$
Find (if possible) the following matrices: \(a, A B\) \(\boldsymbol{b}, B A\) $$A=\left[\begin{array}{ll}2 & 4 \\\3 & 1 \\\4 & 2\end{array}\right], \quad B=\left[\begin{array}{rrr}3 & 2 & 0 \\\\-1 & -3 & 5\end{array}\right]$$
If \(A B=-B A,\) then \(A\) and \(B\) are said to be anticommutative. Are \(A=\left[\begin{array}{rr}0 & -1 \\ 1 & 0\end{array}\right]\) and \(B=\left[\begin{array}{rr}1 & 0 \\ 0 & -1\end{array}\right]\) anticommutative?
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