latihan vectorsandlineartransformation
DESCRIPTION
Latihan VectorsAndLinearTransformationTRANSCRIPT
Peringatan: Setiap bentuk kecurangan dalam bentuk apa pun akan dikenakan sangsi menurut peraturan
akademik!
PROGRAM STUDI TEKNIK INFORMATIKA PRA KUIS BESAR II
Mata Kuliah : Aljabar Linear Kode Kelas : 32 – H dan 32-I Hari, tanggal : 1 April 2013 Dosen : Meifry Manuhutu, S.Si, M.Si Waktu Pengumpulan : 32-H: Senin, 8 April 2013
32-I: Kamis, 11 April 2013
Jawablah pertanyaan berikut dengan tepat dan benar!
1. If possible, find scalars c1, c2, and c3, not all zero, so that
1 2 3
1 1 3 0
2 3 7 0
1 2 4 0
c c c
.
2. If possible, find a, b, and c so that , ,a b cv is orthogonal to both 1,2,1w and 1, 1,1 x .
(10)
3. Which of the following are linear transformations? Andif it is a linear transformation, then find
its standard matrix! (30)
a.
2 3
3 2
2
x x y
L y y z
z z
.
b. , ,2 2L x y x y x .
4. Determine a standard matrix on R3 of linear operator composition of a reflection with respect to
xy- plane, followed by a reflection with respect to xz-plane, followed by an orthogonal
projection with respect to yz-plane. (10)
5. Determine whether the following 3 3:T R R linear transformations defined by the following
equations are one to one transformation. If it is, the find the matrix standard for its invers
operator and determine 1
1 2 3, ,T w w w
1 1 2 3 1 1 2 3
2 1 2 3 2 1 2 3
3 1 2 3 2 3
2 2 3 4
2
2 5
a b
w x x x w x x x
w x x x w x x x
w x x w x x
.(10)
6. Use the substitution scheme and the matrix5 3
2 1
. (30)
a. Code the message WORK HARD.
b. Decode the message 93 36 60 21 159 60 110 43.
God bless your honest handmade!