Tolong dibantu ya dan dijawab dengan benar soal matematika pada gambar !!! yang jago matematika bant.... Question from @nabilaking12

September 2018 1 55 Report

Tolong dibantu ya dan dijawab dengan benar soal matematika pada gambar !!!
yang jago matematika bantuin ya .....

Takamori37 1.
$X\left[\begin{array}{cc}-3&2\\4&5\end{array}\right]=\left[\begin{array}{cc}2&7\\5&8\end{array}\right]+\left[\begin{array}{cc}4&12\\14&10\end{array}\right] \\ \\ X\left[\begin{array}{cc}-3&2\\4&5\end{array}\right]=\left[\begin{array}{cc}6&19\\19&18\end{array}\right] \\ \\ X=\left[\begin{array}{cc}6&19\\19&18\end{array}\right]\left[\begin{array}{cc}-3&2\\4&5\end{array}\right]^{-1} \\ \\ X=\left[\begin{array}{cc}6&19\\19&18\end{array}\right]\frac{1}{-23}\left[\begin{array}{cc}5&-2\\-4&-3\end{array}\right]$

$X=-\frac{1}{23}\left[\begin{array}{cc}6&19\\19&18\end{array}\right]\left[\begin{array}{cc}5&-2\\-4&-3\end{array}\right] \\\\ X=-\frac{1}{23}\left[\begin{array}{cc}30-76&-12-57\\95-72&-38-54\end{array}\right] \\ \\ X=-\frac{1}{23}\left[\begin{array}{cc}-46&-69\\23&-92\end{array}\right] \\ \\ X=\left[\begin{array}{cc}2&3\\-1&4\end{array}\right]$

2.
$\left[\begin{array}{cc}3&-2\\2&-1\end{array}\right]X=\left[\begin{array}{cc}2&3\\4&5\end{array}\right] \\ \\ X=\left[\begin{array}{cc}3&-2\\2&-1\end{array}\right]^{-1}\left[\begin{array}{cc}2&3\\4&5\end{array}\right] \\ \\ X=\frac{1}{1}\left[\begin{array}{cc}-1&2\\-2&3\end{array}\right]\left[\begin{array}{cc}2&3\\4&5\end{array}\right] \\ \\ X=\left[\begin{array}{cc}-2+8&-3+10\\-4+12&-6+15\end{array}\right] \\ \\ X=\left[\begin{array}{cc}6&7\\8&9\end{array}\right]$

3.
$A=\left[\begin{array}{cc}3&5\\2&4\end{array}\right] \\\\ A^{-1}=\frac{1}{12-10}\left[\begin{array}{cc}4&-5\\-2&3\end{array}\right] \\ \\ A^{-1}=\frac{1}{2}\left[\begin{array}{cc}4&-5\\-2&3\end{array}\right] \\ \\ A^{-1}=\left[\begin{array}{cc}2&-\frac{5}{2}\\-1&\frac{3}{2}\end{array}\right]$

4.
$\displaystyle x=\frac{\left|\begin{array}{cc}10&2\\12&3\end{array}\right|}{\left|\begin{array}{cc}4&2\\5&3\end{array}\right|}=\frac{30-24}{12-10}=\frac{6}{2}=3$

5.
$A=\left[\begin{array}{cc}1&-3\\2&5\end{array}\right] \\\\ adj(A)=\left[\begin{array}{cc}5&3\\-2&1\end{array}\right]$

6.
a+b+c = 4
a-2b-c = 1
2a-b-2c = -1
Pada persamaan 1 dan 2, eliminasikan a.
a + b + c = 4
a - 2b - c = 1
- - - Kurangi - - -
3b + 2c = 3
Pada persamaan 2 dan 3, eliminasikan a dengan kalikan 2 persamaan 2
2a - 4b - 2c = 2
2a - b - 2c = -1
- - - Kurangi - - -
-3b = 3
b = -1
Lalu, substitusikan ke 3b+2c = 3
-3 + 2c = 3
2c = 6
c = 3
Lalu, pada persamaan 1:
a+b+c = 4
a-1+3=4
a+2=4
a = 2
Ditanyakan,
a+b = 2+(-1) = 2-1 = 1

7.
3x - 2y = 15
5x + 4y = 3
Eliminasikan y dengan mengalikan persamaan 1 dengan 2
6x - 4y = 30
5x + 4y = 3
- - - Jumlahkan - - -
11x = 33
x = 3
Lalu,
3x - 2y = 15
9 - 2y = 15
2y=9-15
2y = -6
y = -3
Dan,
2x - 5z = 44
6 - 5z = 44
5z = 6-44
5z = -38
z = -38/5
Maka,
x+4y+z = 3+(-3)+(-38/5) = 3-3-38/5
x+4y+z = -38/5

8.
Untuk lebih mudah, ganti:
1/x = a
1/y = b
1/z = c
Menjadi:
4a + 3b + c = 9
3a - 4b + 2c = 3
2a + 5b - c = 5
Eliminasikan c, dengan persamaan 1 dan 3
4a + 3b + c = 9
2a + 5b - c = 5
- - - Jumlahkan- - -
6a+8b = 14
3a + 4b = 7 (i)
Lalu, untuk persamaan 1 dan 2, pers 1 kalikan 2
8a + 6b + 2c = 18
3a - 4b + 2c = 3
- - - Kurangi - - -
5a + 10b = 15
a + 2b = 3 (ii)
Untuk eliminasi b, (ii) kalikan 2
3a + 4b = 7
2a + 4b = 6
- - Kurangi - -
a = 1
Lalu
a + 2b = 3
1 + 2b = 3
2b = 2
b = 1
Dan,
4a + 3b + c = 9
4 + 3 + c = 9
7 + c = 9
c = 9-7
c = 2
Maka,
a = 1
b = 1
c = 2
1/x = 1, diambil x = 1
1/y = 1, diambil y = 1
1/z = 2, diambil z = 1/2
Maka,
12xyz = 12 x 1 x 1 x 1/2
12xyz = 6

9.
7x + 3y = 11700
6x + 5y = 11000
Pers 1 kalikan 5, Pers 2 kalikan 3 agar y tereliminasi
35x + 15y = 58500
18x + 15y = 33000
- - - - Kurangi - - - -
17x = 25500
x = Rp 1.500

10.
a.
y = x^2-4x+8 di absis -1
m = y'
m = 2x - 4
Absis -1
m = -2-4
m = -6
y = x^2-4x+8
y = (-1)^2-4(-1)+8
y = 1+4+8
y = 13
Gradien -6 melalui (-1,13)
y-13 = -6(x+1)
y-13 = -6x-6
6x+y-7 = 0

b.
y = 6/x di ordinat 2
6/x = 2
x = 6/2
x = 3
m = y'
m = -6/x^2
m = -6/3
m = -2
Gradien -2 dan melalui (3,2)
y-2 = -2(x-3)
y-2=-2x+6
2x + y - 8 = 0

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nabilaking12 maksud dari ^ itu kuadrat atau kali ?