Chapter 8: Problem 4
A message written according to a secret code is called a ________.
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Chapter 8: Problem 4
A message written according to a secret code is called a ________.
These are the key concepts you need to understand to accurately answer the question.
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In Exercises 63-70, find (a) \(|A|\), (b) \(|B|\), (c) \(AB\), and (d) \(|AB|\). \(A = \left[ \begin{array}{r} -2 & 1 \\ 4 & -2 \end{array} \right]\), \(B = \left[ \begin{array}{r} 1 & 2 \\ 0 & -1 \end{array} \right]\)
In Exercises 55-62, use the matrix capabilities of a graphing utility to evaluate the determinant. \(\left| \begin{array}{r} 3 & -2 & 4 & 3 & 1 \\ -1 & 0 & 2 & 1 & 0 \\ 5 & -1 & 0 & 3 & 2 \\ 4 & 7 & -8 & 0 & 0 \\ 1 & 2 & 3 & 0 & 2 \end{array} \right|\)
PROPERTIES OF DETERMINANTS In Exercises 97-99, a property of determinants is given (\(A\) and \(B\) are square matrices). State how the property has been applied to the given determinants and use a graphing utility to verify the results. If \(B\) is obtained from \(A\) by interchanging two rows of or interchanging two columns of \(A\), then \(|B| = -|A|\). (a) \(\left| \begin{array}{r} 1 && 3 & 4 \\ -7 && 2 & -5 \\ 6 && 1 & 2 \end{array} \right| = -\left| \begin{array}{r} 1 & 4 && 3 \\ -7 & -5 && 2 \\\ 6 & 2 && 1 \end{array} \right|\) (b) \(\left| \begin{array}{r} 1 && 3 && 4 \\ -2 && 2 && 0 \\ 1 && 6 && 2 \end{array} \right| = -\left| \begin{array}{r} 1 && 6 && 2 \\ -2 && 2 && 0 \\\ 1 && 3 && 4 \end{array} \right|\)
PROPERTIES OF DETERMINANTS In Exercises 97-99, a property of determinants is given (\(A\) and \(B\) are square matrices). State how the property has been applied to the given determinants and use a graphing utility to verify the results. If \(B\) is obtained from \(A\) by multiplying a row by a nonzero constant \(c\) or by multiplying a column by a nonzero constant \(c\), then \(|B| = c|A|\). (a) \(\left| \begin{array}{r} 5 & 10 \\ 2 & -3 \end{array} \right| = 5\left| \begin{array}{r} 1 & 2 \\ 2 & -3 \end{array} \right|\) (b) \(\left| \begin{array}{r} 1 & 8 & -3 \\ 3 & -12 & 6 \\ 7 & 4 & 9 \end{array} \right| = 12\left| \begin{array}{r} 1 & 2 & -1 \\ 3 & -3 & 2 \\\ 7 & 1 & 3 \end{array} \right|\)
In Exercises 17-20, use a graphing utility and Cramer's Ruleto solve (if possible) the system of equations. \(\begin{cases} x + 2y - z = -7 \\ 2x - 2y - 2z = -8 \\ -x + 3y + 4z = 8 \end{cases}\)
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