Question

What is the determinant of

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Answer 1

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

Answer 2

okay

Answer 3

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

Answer 4

please continue

Answer 5

okay

Answer 6

what do you get?

Answer 7

just a second

Answer 8

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

Answer 9

?

Answer 10

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

Answer 11

determinant*

Answer 12

okay i just got confused

Answer 13

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

Answer 14

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

Answer 15

okay

Answer 16

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

Answer 17

-558

Answer 18

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

Answer 19

thank you!

Answer 20

:)