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Berikut ini adalah pertanyaan dari dinsaifuddinma pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

Yang bisa, tolong kerjain yaaaa

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Jawab:

3a.

$P^{2} =\left[\begin{array}{ccc}1&-1\\2&3\end{array}\right] \left[\begin{array}{ccc}1&-1\\2&3\end{array}\right]$

$=\left[\begin{array}{ccc}1(1)+(-1)(2)&1(-1)+(-1)(3)\\2(1)+3(2)&2(-1)+3(3)\end{array}\right]$

$=\left[\begin{array}{ccc}-1&-4\\8&7\end{array}\right]$

$P^{3} = P^{2} \times P$

$=\left[\begin{array}{ccc}-1&-4\\8&7\end{array}\right] \left[\begin{array}{ccc}1&-1\\2&3\end{array}\right]$

$=\left[\begin{array}{ccc}(-1)(1)+(-4)(2)&(-1)(-1)+(-4)(3)\\8(1)+7(2)&8(-1)+7(3)\end{array}\right]$

$=\left[\begin{array}{ccc}-9&-11\\22&13\\\end{array}\right]$

$P^{4} = P^{2} \times P^{2}$

$=\left[\begin{array}{ccc}-1&-4\\8&7\end{array}\right] \left[\begin{array}{ccc}-1&-4\\8&7\end{array}\right]$

$=\left[\begin{array}{ccc}(-1)(-1)+(-4)(8)&(-1)(-4)+(-4)(7)\\8(-1)+7(8)&8(-4)+7(7)\end{array}\right]$

$=\left[\begin{array}{ccc}-31&-24\\48&17\\\end{array}\right]$

$P^{3} - P^{3}+ P^{4}$

$=\left[\begin{array}{ccc}-1&-4\\8&7\end{array}\right]- \left[\begin{array}{ccc}-9&-11\\22&13\end{array}\right]+ \left[\begin{array}{ccc}-31&-24\\48&17\end{array}\right]$

$=\left[\begin{array}{ccc}(-1)-(-9)+(-31)&(-4)-(-11)+(-24)\\8-22+48&7-13+17\end{array}\right]$

$=\left[\begin{array}{ccc}-23&-17\\34&11\\\end{array}\right]$

4a.

$=\left[\begin{array}{ccc}4x-y\\2x+3y\end{array}\right]=\left[\begin{array}{ccc}5\\13\end{array}\right]$

persamaan 1: 4x - y = 5 ==> y = 4x - 5

persamaan 2: 2x + 3y = 13

2x + 3(4x - 5) = 13

2x + 12x - 15 = 13

14x = 28

x = 2

y = 3

$\left[\begin{array}{ccc}x+2y&y+2(-3)\\21+2&-6+2(4)\end{array}\right]=\left[\begin{array}{ccc}2(1)+(-1)(5)&2(2)+(-1)(-1)\\3(1)+4(5)&3(2)+4(-1)\end{array}\right]$