The linear transformation T: R→ Rm is defined by T(v) = Av, where A is as follows. A = 01 -8 1 -16 30 0 1 51 (a) Find T(1, 3, 2, 0). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 2, 0). T(1, 3, 2, 0) = STEP 2: Use your result from Step 1 to solve for T(1, 3, 2, 0). T(1, 3, 2, 0) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 3.5 1 W []
The linear transformation T: R→ Rm is defined by T(v) = Av, where A is as follows. A = 01 -8 1 -16 30 0 1 51 (a) Find T(1, 3, 2, 0). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 2, 0). T(1, 3, 2, 0) = STEP 2: Use your result from Step 1 to solve for T(1, 3, 2, 0). T(1, 3, 2, 0) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 3.5 1 W []
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The linear transformation T: R" → RM is defined by T(v) = Av, where A is as follows.
A =
0 1 -8 1
-1 6 3 0
0 1 5 1
(a) Find T(1, 3, 2, 0).
STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 2, 0).
T(1, 3, 2, 0) =
STEP 2: Use your result from Step 1 to solve for T(1, 3, 2, 0).
4683
T(1, 3, 2, 0) =
(b) Find the preimage of (0, 0, 0).
STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation.
T(w, x, y, z) =
W =
000
X =
y =
z = t
0 1 8 1
-1 6 30
01 5 1
W
X
y
Z
=
Lett be any real number. Set z = t and solve for w, x, and y in terms of t.
0
0
0
STEP 2: Use your result from Step 1 to find the preimage of (0, 0, 0). (Enter each vector as a comma-separated list of its components.)
The preimage is given by the set of vectors {{
): t is any real number}.
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