(Linear Algebra)4.6.1Pls help thanks (b) Find the preimage of (0, 0, 0).STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation.0 1 -9 1T(w, х, у, 2) 3|-1 60 15 1Let t be any real number. Set z = t and solve for w, x, and y in terms of t.W =X =y =z = tSTEP 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}. The linear transformation T: R" → RM is defined by T(v) = Av, where A is as follows.0 1 -9 1A =-1 67 00 15 1(a) Find T(3, 0, 1, 2).STEP 1: Use the definition of T to write a matrix equation for T(3, 0, 1, 2).T(3, о, 1, 2) 3DSTEP 2: Use your result from Step 1 to solve for T(3, 0, 1, 2).T(3, 0, 1, 2) =

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Answered: The linear transformation T: R" → RM is…

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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(Linear Algebra)

6.1

Pls help thanks

(b) Find the preimage of (0, 0, 0).
STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation.
0 1 -9 1
T(w, х, у, 2) 3|
-1 6
0 1
5 1
Let t be any real number. Set z = t and solve for w, x, and y in terms of t.
W =
X =
y =
z = t
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}.

The linear transformation T: R" → RM is defined by T(v) = Av, where A is as follows.
0 1 -9 1
A =
-1 6
7 0
0 1
5 1
(a) Find T(3, 0, 1, 2).
STEP 1: Use the definition of T to write a matrix equation for T(3, 0, 1, 2).
T(3, о, 1, 2) 3D
STEP 2: Use your result from Step 1 to solve for T(3, 0, 1, 2).
T(3, 0, 1, 2) =

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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