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

  2. anonymous
    • one year ago
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    okay

  3. Michele_Laino
    • one year ago
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    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
    • one year ago
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    please continue

  5. anonymous
    • one year ago
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    okay

  6. Michele_Laino
    • one year ago
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    what do you get?

  7. anonymous
    • one year ago
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    just a second

  8. anonymous
    • one year ago
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    (-11 -3) (-10 -14)

  9. anonymous
    • one year ago
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    ?

  10. Michele_Laino
    • one year ago
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    Hint: the determinat of a matrix with real coefficients, has to be a real number

  11. Michele_Laino
    • one year ago
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    determinant*

  12. anonymous
    • one year ago
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    okay i just got confused

  13. Michele_Laino
    • one year ago
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    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
    • one year ago
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    sorry, I developed the determinant along the first column of your matrix, not along the first row

  15. anonymous
    • one year ago
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    okay

  16. Michele_Laino
    • one year ago
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    what is: \[\Large - 62 - \left( {8 \times 62} \right) = ...?\]

  17. anonymous
    • one year ago
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    -558

  18. Michele_Laino
    • one year ago
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    that's right! we have det(A)= -558, where A is your matrix

  19. anonymous
    • one year ago
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    thank you!

  20. Michele_Laino
    • one year ago
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    :)

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