(Linear Algebra)4.6.2Pls help thanks Define the linear transformation I by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T).88433884A =33443(a) ker(T)STEP 1: The kernel of T is given by the solution to the equation T(x) = 0. Let x = (x,, Xa, x,) and find x such that T(x) = 0. (If there are an infinite number ofsolutions use t and s as your parameters.)X =STEP 2: Use your result from Step 1 to find the kernel of T. (If there are an infinite number of solutions use t and s as your parameters.)ker(T) =(b)nullity(T)STEP 3: Use the fact that nullity(T) = dim(ker(T)) to compute nullity(T).(c)range(T)STEP 4: Transpose A and find its equivalent reduced row-echelon form.8884T:44STEP 5: Use your result from Step 4 to find the range of T.ORt is-O {(t, -t, t): t is real}>{(, -+, ;); is rea}-t,OR?(d) rank(T)STEP 6: Use the fact that rank(T) = dim(range(T)) to compute rank(T).

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Answered: Define the linear transformation I by…

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)

6.2

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Define the linear transformation I by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T).
8
8
4
3
3
8
8
4
A =
3
3
4
4
3
(a) ker(T)
STEP 1: The kernel of T is given by the solution to the equation T(x) = 0. Let x = (x,, Xa, x,) and find x such that T(x) = 0. (If there are an infinite number of
solutions use t and s as your parameters.)
X =
STEP 2: Use your result from Step 1 to find the kernel of T. (If there are an infinite number of solutions use t and s as your parameters.)
ker(T) =
(b)
nullity(T)
STEP 3: Use the fact that nullity(T) = dim(ker(T)) to compute nullity(T).
(c)
range(T)
STEP 4: Transpose A and find its equivalent reduced row-echelon form.
8
8
8
4T:
4
4
STEP 5: Use your result from Step 4 to find the range of T.
OR
t is
-
O {(t, -t, t): t is real}
>{(, -+, ;); is rea}
-t,
OR?
(d) rank(T)
STEP 6: Use the fact that rank(T) = dim(range(T)) to compute rank(T).

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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