Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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If \(\det \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} = -15\) then \(\det \begin{bmatrix} d & e & f \\ a & b & c \\ g & h & i \end{bmatrix} =\) [Blank space for answer]. 

### Explanation:
This problem involves calculating the determinants of 3x3 matrices. The given determinant is \(-15\), and you are asked to determine the determinant of a second matrix where two rows have been swapped. In properties of determinants, swapping two rows changes the sign of the determinant. Hence, based on the given determinant, you can calculate the determinant of the second matrix by changing the sign of the first determinant.
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Transcribed Image Text:If \(\det \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} = -15\) then \(\det \begin{bmatrix} d & e & f \\ a & b & c \\ g & h & i \end{bmatrix} =\) [Blank space for answer]. ### Explanation: This problem involves calculating the determinants of 3x3 matrices. The given determinant is \(-15\), and you are asked to determine the determinant of a second matrix where two rows have been swapped. In properties of determinants, swapping two rows changes the sign of the determinant. Hence, based on the given determinant, you can calculate the determinant of the second matrix by changing the sign of the first determinant.
Expert Solution
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Step 1

Given that detabcdefghi=15

We have to find the detdefabcghi

Use the determinant property:- If any two row (or two column) of a determinant are interchanged the value of the determinant is multiplied by -1.

detdefabcghi=1detabcdefghi........(1)

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