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Chapter 6: Problem 62
What is the fastest method for solving a linear system with your graphing utility?
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Determinants are used to write an equation of a line passing through two points. An equation of the line passing through the distinct points \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) is given by $$ \left|\begin{array}{ccc}x & y & 1 \\\x_{1} & y_{1} & 1 \\\x_{2} & y_{2} & 1\end{array}\right|=0 $$ Use this information to work. Use the determinant to write an equation of the line passing through \((-1,3)\) and \((2,4) .\) Then expand the determinant, expressing the line's equation in slope-intercept form.
In Exercises \(27-36,\) find (if possible): \(\begin{array}{llll}\text { a. } A B & \text { and } & \text { b. } B A\end{array}\) $$ A=\left[\begin{array}{rrr} 1 & -1 & 4 \\ 4 & -1 & 3 \\ 2 & 0 & -2 \end{array}\right], \quad B=\left[\begin{array}{rrr} 1 & 1 & 0 \\ 1 & 2 & 4 \\ 1 & -1 & 3 \end{array}\right] $$
Use Cramer's rule to solve each system or to determine that the system is inconsistent or contains dependent equations. $$ \begin{aligned}&2 x=3 y+2\\\&5 x=51-4 y\end{aligned} $$
When expanding a determinant by minors, when is it necessary to supply minus signs?
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. $$ A=\left[\begin{array}{rr} 4 & 0 \\ -3 & 5 \\ 0 & 1 \end{array}\right] \quad B=\left[\begin{array}{rr} 5 & 1 \\ -2 & -2 \end{array}\right] \quad C=\left[\begin{array}{rr} 1 & -1 \\ -1 & 1 \end{array}\right] $$ $$ B C+C B $$
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