## anonymous one year ago What is the determinant of https://lincolnlearningsolutions.brainhoney.com/Resource/19809088,B84/Assets/assessmentimages/alg%202%20pt%202%20u3l5%2019.jpg

1. Michele_Laino

developing the determinant along the first row of your matrix, we have: $\det A = 1 \times \det \left( {\begin{array}{*{20}{c}} { - 5}&{ - 7} \\ { - 5}&{ - 7} \end{array}} \right) - \det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) - 8\det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right)$

2. anonymous

okay

3. Michele_Laino

now we have: $\det \left( {\begin{array}{*{20}{c}} { - 5}&{ - 7} \\ { - 5}&{ - 7} \end{array}} \right) = 0,\;\det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) = 42 + 20 = 62,$

4. Michele_Laino

5. anonymous

okay

6. Michele_Laino

what do you get?

7. anonymous

just a second

8. anonymous

(-11 -3) (-10 -14)

9. anonymous

?

10. Michele_Laino

Hint: the determinat of a matrix with real coefficients, has to be a real number

11. Michele_Laino

determinant*

12. anonymous

okay i just got confused

13. Michele_Laino

hint: $\begin{gathered} \det A = 1 \times \det \left( {\begin{array}{*{20}{c}} { - 5}&{ - 7} \\ { - 5}&{ - 7} \end{array}} \right) - \det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) - 8\det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) = \hfill \\ \hfill \\ = 0 - 62 - 8 \times 62 = ...? \hfill \\ \end{gathered}$

14. Michele_Laino

sorry, I developed the determinant along the first column of your matrix, not along the first row

15. anonymous

okay

16. Michele_Laino

what is: $\Large - 62 - \left( {8 \times 62} \right) = ...?$

17. anonymous

-558

18. Michele_Laino

that's right! we have det(A)= -558, where A is your matrix

19. anonymous

thank you!

20. Michele_Laino

:)

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