Define the linear transformation T by T(x) = Ax. 2 A-[1-13] 0 12 = (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) ker(7) = {-4t, — 2t,t X (b) Find the range of T. O {(2t, t): t is any real number} OR O {(-t, t): t is any real number} R² O {(t, 2t): t is any real number}
Define the linear transformation T by T(x) = Ax. 2 A-[1-13] 0 12 = (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) ker(7) = {-4t, — 2t,t X (b) Find the range of T. O {(2t, t): t is any real number} OR O {(-t, t): t is any real number} R² O {(t, 2t): t is any real number}
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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![Define the linear transformation T by T(x) = Ax.
2
A-[1-13]
0
12
=
(a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.)
ker(7) = {-4t, — 2t,t
X
(b) Find the range of T.
O {(2t, t): t is any real number}
OR
O {(-t, t): t is any real number}
R²
O {(t, 2t): t is any real number}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b8a4ad9-b66e-4dbe-8b3f-39bf0adb3cae%2F1161a153-7aa9-4eba-a80e-d61b3438ee47%2Fes31w4_processed.png&w=3840&q=75)
Transcribed Image Text:Define the linear transformation T by T(x) = Ax.
2
A-[1-13]
0
12
=
(a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.)
ker(7) = {-4t, — 2t,t
X
(b) Find the range of T.
O {(2t, t): t is any real number}
OR
O {(-t, t): t is any real number}
R²
O {(t, 2t): t is any real number}
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