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Soal Latihan Aljabar Linear
Pertemuan 9
Perkalian Matriks 2D
Soal 1
Diberikan dua matriks \(A\) dan
\(B\) :\[
A = \begin{bmatrix} \lambda & 2 \\ 3 & \lambda \end{bmatrix},
\quad B = \begin{bmatrix} 1 & 4 \\ 2 & \lambda \end{bmatrix}
\]
Hitunglah hasil perkalian \(A \cdot
B\) dan tentukan persamaan yang terbentuk dari elemen-elemen
matriks hasil perkalian tersebut.
Soal 2
Diberikan dua matriks \(C\) dan
\(D\) :\[
C = \begin{bmatrix} \lambda+1 & 3 \\ 2 & \lambda-1
\end{bmatrix}, \quad D = \begin{bmatrix} 4 &\lambda \\ 1 & 5
\end{bmatrix}
\]
Hitunglah hasil perkalian \(C \cdot
D\) dan tentukan persamaan kuadrat yang terbentuk dari
elemen-elemen matriks hasil perkalian tersebut.
Soal 3
Diberikan dua matriks \(E\) dan
\(F\) :\[
E = \begin{bmatrix} x & 1 \\ 4 & x-2 \end{bmatrix}, \quad F =
\begin{bmatrix} 3 & x \\ 2 & 4 \end{bmatrix}
\]
Hitunglah hasil perkalian \(E \cdot
F\) dan tentukan persamaan kuadrat yang terbentuk dari
elemen-elemen matriks hasil perkalian tersebut.
Determinan Matriks 2D
Soal 7
Diberikan matriks \(G\) :
\[
G = \begin{bmatrix} 6 & 2 \\ 4 & 3 \end{bmatrix}
\]
Hitunglah determinan dari matriks \(G\) !
Soal 8
Diberikan matriks \(H\) :\[
H = \begin{bmatrix} \lambda & 2 \\ 3 & \lambda \end{bmatrix}
\]
Hitung determinan dari matriks \(H\) , kemudian tentukan nilai \(\lambda\) jika determinan tersebut sama
dengan nol.
Soal 9
Diberikan matriks \(I\) :\[
I = \begin{bmatrix} \lambda + 2 & 5 \\ 4 & \lambda - 3
\end{bmatrix}
\]
Hitung determinan dari matriks \(I\) , kemudian tentukan nilai \(\lambda\) jika determinan tersebut sama
dengan nol.
Determinan Matriks 3D
Soal 10
Diberikan matriks \(J\) :\[
J = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8
& 9 \end{bmatrix}
\]
Hitunglah determinan dari matriks \(J\) menggunakan ekspansi kofaktor!
Soal 11
Diberikan matriks \(K\) :
\[
K = \begin{bmatrix} \lambda & 1 & 2 \\ 0 & \lambda & 3
\\ 1 & 2 & \lambda \end{bmatrix}
\]
Hitung determinan dari matriks \(K\) , kemudian tentukan nilai \(\lambda\) jika determinan tersebut sama
dengan nol.
Soal 12
Diberikan matriks \(L\) :\[
L = \begin{bmatrix} 2 & 4 & \lambda \\ 1 & \lambda & 5
\\ \lambda & 3 & 6 \end{bmatrix}
\]
Hitung determinan dari matriks \(L\) , kemudian tentukan nilai \(\lambda\) jika determinan tersebut sama
dengan nol.
Invers Matriks 2D
Soal 13
Diberikan matriks \(M\) :\[
M = \begin{bmatrix} 3 & 4 \\ 2 & 1 \end{bmatrix}
\]
Hitunglah invers dari matriks \(M\) ,
jika ada.
Soal 14
Diberikan matriks \(N\) :\[
N = \begin{bmatrix} x & 5 \\ 1 & 2 \end{bmatrix}
\]
Hitunglah invers dari matriks \(N\) ,
jika ada, dan tentukan nilai \(x\) agar
matriks \(B\) memiliki invers.
Soal 15
Diberikan matriks \(O\) :\[
O = \begin{bmatrix} 1 & 3 \\ 2 & 5 \end{bmatrix}
\]
Hitunglah invers dari matriks \(O\) ,
jika ada.
Invers Matriks 3D
Soal 16
Diberikan matriks \(P\) :\[
P = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6
& 0 \end{bmatrix}
\]
Hitunglah invers dari matriks \(P\) ,
jika ada.
Soal 17
Diberikan matriks \(Q\) :\[
Q = \begin{bmatrix} 2 & 0 & 1 \\ 1 & 3 & 2 \\ 0 & 1
& 4 \end{bmatrix}
\]
Hitunglah invers dari matriks \(Q\) ,
jika ada.
Soal 18
Diberikan matriks \(R\) :\[
R = \begin{bmatrix} x & 1 & 2 \\ 0 & x & 3 \\ 4 & 5
& x \end{bmatrix}
\]
Hitunglah invers dari matriks \(R\) ,
jika ada, dan tentukan nilai \(x\) agar
matriks \(R\) memiliki invers.
Sistem Persamaan Linear 2D
Soal 19
Diberikan sistem persamaan linear berikut:\[
\begin{aligned}
3x + 2y &= 8, \\
5x - y &= 7.
\end{aligned}
\]
Selesaikan sistem persamaan tersebut menggunakan metode eliminasi
atau substitusi.
Soal 20
Diberikan sistem persamaan linear berikut:\[
\begin{aligned}
2x - 3y &= 5, \\
4x + y &= 11.
\end{aligned}
\]
Selesaikan sistem persamaan tersebut menggunakan metode matriks atau
metode substitusi.
Soal 21
Diberikan sistem persamaan linear berikut:\[
\begin{aligned}
x + 4y &= 12, \\
3x - 2y &= 4.
\end{aligned}
\]
Selesaikan sistem persamaan tersebut dengan metode eliminasi atau
substitusi.
Sistem Persamaan Linear 3D
Soal 22
Diberikan sistem persamaan linear berikut:\[
\begin{aligned}
x + 2y + 3z &= 9, \\
4x + 5y + 6z &= 22, \\
7x + 8y + 9z &= 39.
\end{aligned}
\]
Selesaikan sistem persamaan tersebut menggunakan metode eliminasi
atau metode invers matriks.
Soal 23
Diberikan sistem persamaan linear berikut:\[
\begin{aligned}
2x - y + 3z &= 7, \\
x + 4y + z &= 4, \\
3x - 2y + 2z &= 5.
\end{aligned}
\]
Selesaikan sistem persamaan tersebut menggunakan metode substitusi
atau metode invers matriks.
Soal 24
Diberikan sistem persamaan linear berikut:\[
\begin{aligned}
x + y + z &= 6, \\
2x + 3y - z &= 3, \\
4x - y + 2z &= 8.
\end{aligned}
\]
Selesaikan sistem persamaan tersebut menggunakan metode eliminasi
atau metode invers matriks.
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aWthIGFkYS4gIAoKLS0tCgojIyBTb2FsIDE4ICAKCkRpYmVyaWthbiBtYXRyaWtzICRSJDogIAokJApSID0gXGJlZ2lue2JtYXRyaXh9IHggJiAxICYgMiBcXCAwICYgeCAmIDMgXFwgNCAmIDUgJiB4IFxlbmR7Ym1hdHJpeH0KJCQgIAoKSGl0dW5nbGFoIGludmVycyBkYXJpIG1hdHJpa3MgJFIkLCBqaWthIGFkYSwgZGFuIHRlbnR1a2FuIG5pbGFpICR4JCBhZ2FyIG1hdHJpa3MgJFIkIG1lbWlsaWtpIGludmVycy4gIAoKIyBTaXN0ZW0gUGVyc2FtYWFuIExpbmVhciAyRAoKIyMgU29hbCAxOSAgCgpEaWJlcmlrYW4gc2lzdGVtIHBlcnNhbWFhbiBsaW5lYXIgYmVyaWt1dDogIAokJApcYmVnaW57YWxpZ25lZH0KM3ggKyAyeSAmPSA4LCBcXAo1eCAtIHkgJj0gNy4KXGVuZHthbGlnbmVkfQokJCAgCgpTZWxlc2Fpa2FuIHNpc3RlbSBwZXJzYW1hYW4gdGVyc2VidXQgbWVuZ2d1bmFrYW4gbWV0b2RlIGVsaW1pbmFzaSBhdGF1IHN1YnN0aXR1c2kuICAKCi0tLQoKIyMgU29hbCAyMCAgCgpEaWJlcmlrYW4gc2lzdGVtIHBlcnNhbWFhbiBsaW5lYXIgYmVyaWt1dDogIAokJApcYmVnaW57YWxpZ25lZH0KMnggLSAzeSAmPSA1LCBcXAo0eCArIHkgJj0gMTEuClxlbmR7YWxpZ25lZH0KJCQgIAoKU2VsZXNhaWthbiBzaXN0ZW0gcGVyc2FtYWFuIHRlcnNlYnV0IG1lbmdndW5ha2FuIG1ldG9kZSBtYXRyaWtzIGF0YXUgbWV0b2RlIHN1YnN0aXR1c2kuICAKCi0tLQoKIyMgU29hbCAyMSAgCgpEaWJlcmlrYW4gc2lzdGVtIHBlcnNhbWFhbiBsaW5lYXIgYmVyaWt1dDogIAokJApcYmVnaW57YWxpZ25lZH0KeCArIDR5ICY9IDEyLCBcXAozeCAtIDJ5ICY9IDQuClxlbmR7YWxpZ25lZH0KJCQgIAoKU2VsZXNhaWthbiBzaXN0ZW0gcGVyc2FtYWFuIHRlcnNlYnV0IGRlbmdhbiBtZXRvZGUgZWxpbWluYXNpIGF0YXUgc3Vic3RpdHVzaS4gIAoKIyBTaXN0ZW0gUGVyc2FtYWFuIExpbmVhciAzRAoKIyMgU29hbCAyMiAgCgpEaWJlcmlrYW4gc2lzdGVtIHBlcnNhbWFhbiBsaW5lYXIgYmVyaWt1dDogIAokJApcYmVnaW57YWxpZ25lZH0KeCArIDJ5ICsgM3ogJj0gOSwgXFwKNHggKyA1eSArIDZ6ICY9IDIyLCBcXAo3eCArIDh5ICsgOXogJj0gMzkuClxlbmR7YWxpZ25lZH0KJCQgIAoKU2VsZXNhaWthbiBzaXN0ZW0gcGVyc2FtYWFuIHRlcnNlYnV0IG1lbmdndW5ha2FuIG1ldG9kZSBlbGltaW5hc2kgYXRhdSBtZXRvZGUgaW52ZXJzIG1hdHJpa3MuICAKCi0tLQoKIyMgU29hbCAyMyAgCgpEaWJlcmlrYW4gc2lzdGVtIHBlcnNhbWFhbiBsaW5lYXIgYmVyaWt1dDogIAokJApcYmVnaW57YWxpZ25lZH0KMnggLSB5ICsgM3ogJj0gNywgXFwKeCArIDR5ICsgeiAmPSA0LCBcXAozeCAtIDJ5ICsgMnogJj0gNS4KXGVuZHthbGlnbmVkfQokJCAgCgpTZWxlc2Fpa2FuIHNpc3RlbSBwZXJzYW1hYW4gdGVyc2VidXQgbWVuZ2d1bmFrYW4gbWV0b2RlIHN1YnN0aXR1c2kgYXRhdSBtZXRvZGUgaW52ZXJzIG1hdHJpa3MuICAKCi0tLQoKIyMgU29hbCAyNCAgCgpEaWJlcmlrYW4gc2lzdGVtIHBlcnNhbWFhbiBsaW5lYXIgYmVyaWt1dDogIAokJApcYmVnaW57YWxpZ25lZH0KeCArIHkgKyB6ICY9IDYsIFxcCjJ4ICsgM3kgLSB6ICY9IDMsIFxcCjR4IC0geSArIDJ6ICY9IDguClxlbmR7YWxpZ25lZH0KJCQgIAoKU2VsZXNhaWthbiBzaXN0ZW0gcGVyc2FtYWFuIHRlcnNlYnV0IG1lbmdndW5ha2FuIG1ldG9kZSBlbGltaW5hc2kgYXRhdSBtZXRvZGUgaW52ZXJzIG1hdHJpa3Mu
