Tugas Aljabar Linear
19 October 2016 18:40:39
Dibaca : 1418
Kategori : Tugas Mahasiswa
Berikut tugas Aljabar Linear untuk Mahasiswa Matematika semester 1.
1. Selesaikan sistem berikut dengan Eliminasi Gauss
a) | 10y | - | 4z | + | w | = | 1 | b) | x | - | 2y | + | z | - | 4w | = | 1 | ||
x | + | 4y | - | z | + | w | = | 2 | x | + | 3y | + | 7z | + | 2w | = | 2 | ||
3x | + | 2y | + | z | + | 2w | = | 5 | x | - | 12y | - | 11z | - | 16w | = | 5 | ||
-2x | - | 8y | + | 2z | - | 2w | = | -4 | |||||||||||
x | - | 6y | + | 3z | = | 1 |
2. Selesaikan soal no.1 dengan metode Gauss-Jordan
3. Selesaikan sistem homogen berikut
a) | 2x | + | y | + | 3z | = | 0 | b) | x | + | y | + | x | = | 0 | ||||
x | + | 2y | = | 0 | -v | - | w | + | 2x | - | 3y | + | x | = | 0 | ||||
y | + | z | = | 0 | v | + | w | - | 2x | - | x | = | 0 | ||||||
2v | + | 2w | - | x | + | x | = | 0 |
4. Untuk nilai a berapakah sistem berikut tidak memiliki solusi? Tepat satu solusi? Takhingga banyaknya solusi?
x | + | 2y | - | 3z | = | 4 |
3x | - | y | + | 5z | = | 2 |
4x | + | y | + | (a^2-14)z | = | a+2 |
5. Reduksilah matriks berikut menjadi bentuk eselon baris tereduksi tanpa menggunakan bentuk pecahan apapun.
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