Problem 2. Let T: R3→ R³ be a linear transformation such that (E)-E T. and T (a) Find the matrix A of T, and use it to give the explicit formula for T. -12r1+3r2 +8r3 10z1 – 3r2 – 4r3 -10r1+3r2+5x3] e: T %3D 12r1 +3r2+8x3 7x1-2r2-3r3 –10r1+3r2+ 5rs 2: T [-15z1 + 4r2 + 9x3 10r1-3r2- 4r3 -10r1 +3r2 + 5r3 Г: Т V: None of the other answers. (b) (Continuation of Problem 2) [2r1 +13 Define a linear transformation S: R→R³ by the formula S(7) = T(-27)+ 12-13 where = |I2 %3D Find the matrix B of S. 26 -6 -15] e: B=-20 21 -5 -10 13 -6 -157 2: B=-20 -7 9. 21 3 [1 0 0] T: B 0 10 00 1 V: None of the other answers.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 2. Let T: R → R³ be a linear transformation such that
(E)-H-()-E
(E)-E
and T
(a) Find the matrix A of T, and use it to give the explicit formula for T.
[-12r1 + 3r2 + 8r3
10z1 – 3r2 – 4r3
-10z1+3r2+5x3]
Ө:Т
-12r1 + 3r2 + 8r3]
7x1 – 2r2 – 3r3
-10r1 + 3r2 + 5x3
N: T
12
(E)-E
-1521 + 4x2 + 9x3]
10r1-3r2- 4r3
-10r1+3r2 + 5r3]
T: T
V: None of the other answers.
(b) (Continuation of Problem 2)
[2r1 +13]
Define a linear transformation S: R → R³ by the formula S(F) = T(-27)+| 12 - 13, where i =
I2
Find the matrix B of S.
26
-6 -15
e: B=-20
21
-5 -10
13
-6 -15
N: B=
-20 -7
2
21
3
[1 0
T: B=0
0 0
V: None of the other answers.
or
Transcribed Image Text:Problem 2. Let T: R → R³ be a linear transformation such that (E)-H-()-E (E)-E and T (a) Find the matrix A of T, and use it to give the explicit formula for T. [-12r1 + 3r2 + 8r3 10z1 – 3r2 – 4r3 -10z1+3r2+5x3] Ө:Т -12r1 + 3r2 + 8r3] 7x1 – 2r2 – 3r3 -10r1 + 3r2 + 5x3 N: T 12 (E)-E -1521 + 4x2 + 9x3] 10r1-3r2- 4r3 -10r1+3r2 + 5r3] T: T V: None of the other answers. (b) (Continuation of Problem 2) [2r1 +13] Define a linear transformation S: R → R³ by the formula S(F) = T(-27)+| 12 - 13, where i = I2 Find the matrix B of S. 26 -6 -15 e: B=-20 21 -5 -10 13 -6 -15 N: B= -20 -7 2 21 3 [1 0 T: B=0 0 0 V: None of the other answers. or
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