1. Diketahui matriks
$P=\begin{bmatrix}4&-2\\2x-2&4\\\end{bmatrix}$
Jika det $P$ adalah 2, berapakah nilai dari $x$?
a. $\frac{2}{9}$
b. $-\frac{9}{2}$
c. $\frac{9}{2}$
d. $-\frac{2}{9}$
e. $\frac{9}{4}$
Rumus determinan = $ad - bc$
$\begin{bmatrix}a&b\\c&d\\\end{bmatrix}$
sedangkan diketahui bahwa determinan $P$ adalah 2. Maka..
$\begin{bmatrix}4&-2\\2x-2&4\\\end{bmatrix}=2$
$(4\times4)-(-2(2x-2))=2$
$16 - (-4x+4)=2$
$16 - 4x +4 = 2$
$-4x = -18$
$x = \frac{9}{2}$
2. Matriks $A=\begin{bmatrix}4&0\\0&3\\\end{bmatrix}$ dan $B$ adalah matriks berukuran 2 x 2. Jika det($B$) = $b$, maka det($AB$)
a. $12b$
b. $6b$
c. $3b$
d. $9b$
e. $10b$
Jawaban : A
det($AB$)= det $a$ x det $b$
det$A$= (4 * 3)(0 * 0)
det$A$= 12
det($AB$)= 12 x b = 12b
3. Inverse dari matriks A = $\begin{bmatrix}6&5\\3&4\\\end{bmatrix}$ adalah...
a. $\begin{bmatrix}\frac{4}{9}&-\frac{5}{9}\\-\frac{1}{3}&\frac{2}{3}\\\end{bmatrix}$
b. $\begin{bmatrix}\frac{5}{9}&-\frac{4}{9}\\-\frac{2}{3}&\frac{1}{3}\\\end{bmatrix}$
c. $\begin{bmatrix}\frac{1}{9}&-\frac{2}{9}\\-\frac{5}{3}&\frac{4}{3}\\\end{bmatrix}$
d. $\begin{bmatrix}\frac{5}{9}&-\frac{4}{9}\\-\frac{1}{3}&\frac{2}{3}\\\end{bmatrix}$
Jawaban : A
$\begin{bmatrix}a&b\\c&d\\\end{bmatrix}$
Invers : $\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\\\end{bmatrix}$
$=\frac{1}{9}\times\begin{bmatrix}4&-5\\-3&6\\\end{bmatrix}$
$=\begin{bmatrix}\frac{4}{9}&-\frac{5}{9}\\-\frac{1}{3}&\frac{2}{3}\\\end{bmatrix}$
4. Diketahui matriks $B = \begin{bmatrix}1&6\\4&3\\\end{bmatrix}$. Maka $B^{T}$ adalah...
a.
b.
c. $\begin{bmatrix}1&4\\6&3\\\end{bmatrix}$
d.
e.
Jawaban : C
$B^{T}$ = $B$ transpose
$\begin{bmatrix}a&b\\c&d\\\end{bmatrix} = \begin{bmatrix}&6\\4&3\\\end{bmatrix}$
B transpose = $\begin{bmatrix}a&c\\b&d\\\end{bmatrix}$
= $\begin{bmatrix}1&4\\6&3\\\end{bmatrix}$
5.
