latihan vectorsandlineartransformation

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!