Question

Diketahui matriks A = (1 -s q 3), B = (4 -5 -3 q), dan C = (3r -5r 1-p 3p-1) Jika B-A=C^T
, maka tentukan |C|³!​

Answer 1

MaTRiKs

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[tex]B - A = C^{T}[/tex]

[tex]\left[\begin{array}{ccc}4&-5\\-3&q\end{array}\right] - \left[\begin{array}{ccc}1&-s\\q&3\end{array}\right] = \left[\begin{array}{ccc}3r&1-p\\-5r&3p-1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}3&-5+s\\-3-q&q-3\end{array}\right] = \left[\begin{array}{ccc}3r&1-p\\-5r&3p-1\end{array}\right][/tex]

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selidiki variabel yang sejenis,

3r = 3

 r = 1

-3 - q = -5r

-3 - q = -5

      q = 2

3p - 1 = q - 3

3p - 1 = 2 - 3

   3p = -1 + 1

     p = 0

-5 + s = 1 - p

-5 + s = 1 - 0

      s = 6

Sehingga,

[tex]C = \left[\begin{array}{ccc}3&-5\\1&-1\end{array}\right][/tex]

|C| = 3(1) - 1(-5)

|C| = 3 + 5

|C| = 8 → |C|³ = 8³ = 512

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