Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Given a matrix \( M = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \) and that \(\det(M) = 4\). Find the following determinants: 1. \(\det\left(\begin{bmatrix} 2a & 2b & 2c \\ d & e & f \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 2. \(\det\left(\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 3. \(\det\left(\begin{bmatrix} g & h & i \\ d & e & f \\ a & b & c \end{bmatrix}\right) = \boxed{}\) 4. \(\det\left(\begin{bmatrix} a & b & c \\ a & b & c \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 5. \(\det\left(\begin{bmatrix} a+2d & b+2e & c+2f \\ d & e & f \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 6. \(\det(M^{-1}) = \boxed{}\)
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Transcribed Image Text:Given a matrix \( M = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \) and that \(\det(M) = 4\). Find the following determinants: 1. \(\det\left(\begin{bmatrix} 2a & 2b & 2c \\ d & e & f \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 2. \(\det\left(\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 3. \(\det\left(\begin{bmatrix} g & h & i \\ d & e & f \\ a & b & c \end{bmatrix}\right) = \boxed{}\) 4. \(\det\left(\begin{bmatrix} a & b & c \\ a & b & c \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 5. \(\det\left(\begin{bmatrix} a+2d & b+2e & c+2f \\ d & e & f \\ g & h & i \end{bmatrix}\right) = \boxed{}\) 6. \(\det(M^{-1}) = \boxed{}\)
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