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 2 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) = 3. (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 4 4 STEP 5: Use your result from Step 4 to find the range of T. OR
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 2 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) = 3. (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 4 4 STEP 5: Use your result from Step 4 to find the range of T. OR
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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(
4.
6.2
Pls help thanks
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a7c37e1-d117-46e5-8cc2-cb36983cacd6%2F5ee4c515-9378-44a0-ae08-e5687d9e5246%2Fhb5kt3k_processed.png&w=3840&q=75)
Transcribed Image Text: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).
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