||
Membaca
SIMAK UI 2010

Solusi SIMAK UI 2010 Kode 209 Nomor 11


Misalkan\ P=\begin{bmatrix} p & q \\ r & s \end{bmatrix}.
Jika\ P^{-1}=2P^{T},\ maka\ ps-qr=....
(A)\,\,\, 1\ atau\ \sqrt{2}
(B)\,\,\, -\frac{1}{2}\ atau\ \frac{1}{2}
(C)\,\,\, -\frac{1}{2}\sqrt{2}\ atau\ \frac{1}{2}\sqrt{2}
(D)\,\,\, -\sqrt{2}\ atau\ \sqrt{2}
(E)\,\,\, -1\ atau\ 1
Jawaban: B

P^{-1}=2P^{T}
\frac{1}{ps-qr}\begin{bmatrix} s & -q \\ -r & p \end{bmatrix}=2\begin{bmatrix} p & r \\ q & s \end{bmatrix}
\frac{s}{ps-qr}=2p \qquad \rightarrow \qquad ps-qr=\frac{s}{2p}\,\, .................\,\, (1)
\frac{p}{ps-qr}=2s\,\, .................\,\, (2)
Dari (*) dan (**) diperoleh:

\frac{p}{\frac{s}{2p}}=2s
2p^2=2s^2
p^2=s^2
p=\pm \sqrt{s^2}
p=\pm s\,\, .................\,\, (3)
Substitusi (3) ke (1) menghasilkan:

ps-qr=\frac{s}{2 \pm s}=\frac{1}{\pm 2}=\pm \frac{1}{2}

About Kalakay

Guru Matematika SMK

Diskusi

Belum ada komentar.

Tinggalkan Balasan

Isikan data di bawah atau klik salah satu ikon untuk log in:

Logo WordPress.com

You are commenting using your WordPress.com account. Logout / Ubah )

Gambar Twitter

You are commenting using your Twitter account. Logout / Ubah )

Foto Facebook

You are commenting using your Facebook account. Logout / Ubah )

Foto Google+

You are commenting using your Google+ account. Logout / Ubah )

Connecting to %s

%d blogger menyukai ini: