KuMat (Kuis Matematika)

Materi : SPLDV dalam matriks

nilai x dan y berturut-turut yang memenuhi persamaan berikut :
$binom{2 : 3}{5 : 4} binom{x}{y} = binom{2}{12}$
perlu diingat sebelumnya :
$jika : \ binom{a : b}{p : q} binom{x}{y} = binom{c}{r} \ maka : \ binom{x}{y} = frac{1}{aq - bp} binom{q : - b}{ - p : a} binom{c}{r}$

KuMat (Kuis Matematika)

Jawab:

(4,-2)

Penjelasan dengan langkah-langkah:

$displaystyle left[begin{array}{ccc}2&3\5&4end{array}right] left[begin{array}{ccc}x\yend{array}right] = 2left[begin{array}{ccc}1\6end{array}right]\ left[begin{array}{ccc}x\yend{array}right] = 2cdot left[begin{array}{ccc}2&3\5&4end{array}right]^{-1}cdot left[begin{array}{ccc}1\6end{array}right]$

$left[begin{array}{ccc}x\yend{array}right] = dfrac{2}{2cdot 4-3cdot 5}cdot left[begin{array}{ccc}4&-3\-5&2end{array}right]cdot left[begin{array}{ccc}1\6end{array}right]\left[begin{array}{ccc}x\yend{array}right] = dfrac{2}{7}cdot left[begin{array}{ccc}-4&3\5&-2end{array}right]cdot left[begin{array}{ccc}1\6end{array}right]$

$left[begin{array}{ccc}x\yend{array}right] = dfrac{2}{7}cdot left(1cdotleft[begin{array}{ccc}-4\5end{array}right]+ 6cdot left[begin{array}{ccc}3\-2end{array}right]right)\\left[begin{array}{ccc}x\yend{array}right] = dfrac{2}{7}cdot left[begin{array}{ccc}14\-7end{array}right]\\\boxed{boxed{left[begin{array}{ccc}x\yend{array}right] = left[begin{array}{ccc}4\-2end{array}right]}}$

Penjelasan dengan langkah-langkah:

$left[begin{array}{ccc}2&3\5&4\end{array}right] left[begin{array}{ccc}x\y\end{array}right] =left[begin{array}{ccc}2\12\end{array}right] \\\D=left[begin{array}{ccc}2&3\5&4\end{array}right] \\\=2(4)-3(5)\\=8 - 15\\= -7\\\Dx=left[begin{array}{ccc}2&3\12&4\end{array}right] \\\=2(4)-3(12)\\= -28\\\Dy=left[begin{array}{ccc}2&2\5&12\end{array}right] \\\= 2(12)-2(5)\\= 24-10\\= 14\$

x = -28/-7

= 4

y = 14/-7

= -2

Sehingga penyelesaian x = 4 dan y = -2