The linear transformation T: P2 → R is defined as T(ax? + bx + c) = a. Determine ker(T). Explain.
The linear transformation T: P2 → R is defined as T(ax? + bx + c) = a. Determine ker(T). Explain.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 22EQ
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![The linear transformation T: P2 → R is defined as
T(ax2 + bx + c) = a.
Determine ker(T). Explain.
Consider the linear transformation T: P2 → Pq defined by
T(a + bx + cx²) = a + (b+ c)x.
Compute the standard matrix [T]B'++B for T with respect to the basis
B = {2 – x + x², 1+x +x², 2 – 3x}
for P2 and the basis B' = {3,1+2x} for P1. Explain, and show your steps.
Given that
3
1
3
-3
3 1
=
1
1
0 -3
3
find an explicit formula for
-3
for any non-negative integer n.
2 -4
An inner product on R² is defined as
(u, v) = (Au) · (Av),
3
where A =
2
2 -3
Is (1, –2) orthogonal to (4, 2) with respect to this inner product? Explain.
Find d(5x, 7y), where x = (1, –1), and y = (0, 1).
(a)
(b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F925e5093-3a55-48a8-a626-298affe212e1%2Ff9a8d909-6129-4894-aaaf-b17bb40f06b0%2Flql917_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The linear transformation T: P2 → R is defined as
T(ax2 + bx + c) = a.
Determine ker(T). Explain.
Consider the linear transformation T: P2 → Pq defined by
T(a + bx + cx²) = a + (b+ c)x.
Compute the standard matrix [T]B'++B for T with respect to the basis
B = {2 – x + x², 1+x +x², 2 – 3x}
for P2 and the basis B' = {3,1+2x} for P1. Explain, and show your steps.
Given that
3
1
3
-3
3 1
=
1
1
0 -3
3
find an explicit formula for
-3
for any non-negative integer n.
2 -4
An inner product on R² is defined as
(u, v) = (Au) · (Av),
3
where A =
2
2 -3
Is (1, –2) orthogonal to (4, 2) with respect to this inner product? Explain.
Find d(5x, 7y), where x = (1, –1), and y = (0, 1).
(a)
(b)
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