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

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

Mathematics
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developing the determinant along the first row of your matrix, we have: \[ \det A = 1 \times \det \left( {\begin{array}{*{20}{c}} { - 5}&{ - 7} \\ { - 5}&{ - 7} \end{array}} \right) - \det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) - 8\det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right)\]
okay
now we have: \[\det \left( {\begin{array}{*{20}{c}} { - 5}&{ - 7} \\ { - 5}&{ - 7} \end{array}} \right) = 0,\;\det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) = 42 + 20 = 62,\]

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Other answers:

please continue
okay
what do you get?
just a second
(-11 -3) (-10 -14)
?
Hint: the determinat of a matrix with real coefficients, has to be a real number
determinant*
okay i just got confused
hint: \[\begin{gathered} \det A = 1 \times \det \left( {\begin{array}{*{20}{c}} { - 5}&{ - 7} \\ { - 5}&{ - 7} \end{array}} \right) - \det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) - 8\det \left( {\begin{array}{*{20}{c}} { - 6}&4 \\ { - 5}&{ - 7} \end{array}} \right) = \hfill \\ \hfill \\ = 0 - 62 - 8 \times 62 = ...? \hfill \\ \end{gathered} \]
sorry, I developed the determinant along the first column of your matrix, not along the first row
okay
what is: \[\Large - 62 - \left( {8 \times 62} \right) = ...?\]
-558
that's right! we have det(A)= -558, where A is your matrix
thank you!
:)

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