Let T:P2(R) → P2(R) T(a + bx + cz?) = 3a – 16 + 6c + ( – 1la + 4b – 22c)z + (– 6a + 36 – 1lc)z? Let B = {1 – 2x – 42², 1 – 1z – 2z°, 0 + Oz + 1z²} and C = {- 8 – 27 – 3z², 0 + 1z + 0z², 3 + 0r + 1z²} be two bases for p2(R). Compute the matrix [T]% = M,M2M3 using change of basis to get each of the three matrices below.
Let T:P2(R) → P2(R) T(a + bx + cz?) = 3a – 16 + 6c + ( – 1la + 4b – 22c)z + (– 6a + 36 – 1lc)z? Let B = {1 – 2x – 42², 1 – 1z – 2z°, 0 + Oz + 1z²} and C = {- 8 – 27 – 3z², 0 + 1z + 0z², 3 + 0r + 1z²} be two bases for p2(R). Compute the matrix [T]% = M,M2M3 using change of basis to get each of the three matrices below.
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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![Let T:p2(IR) → P2(R)
T(a + bæ + cz?) = 3a – 1b + 6c + (– 11a + 4b – 22c)x + ( – 6a + 36 – 11c)z?
Let B = {1 – 2x –- 4x², 1 – læ – 22², 0 + 0æ + læ²} and
C = { - 8 – 22 – 3æ², 0 + læ + 0z², 3 + 0æ + læ²} be two bases for p2(R).
Compute the matrix [T]% = M1M2M3 using change of basis to get each of the three matrices below.
(You may use a matrix inverse calculator to determine any required inverses of matrices.):
M1 =
M2
M3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03cf2bd3-2adf-4171-ac75-47086170b0a6%2F7ee8fbba-9f8b-4173-afa0-86d5880017d2%2Fv0380zc_processed.png&w=3840&q=75)
Transcribed Image Text:Let T:p2(IR) → P2(R)
T(a + bæ + cz?) = 3a – 1b + 6c + (– 11a + 4b – 22c)x + ( – 6a + 36 – 11c)z?
Let B = {1 – 2x –- 4x², 1 – læ – 22², 0 + 0æ + læ²} and
C = { - 8 – 22 – 3æ², 0 + læ + 0z², 3 + 0æ + læ²} be two bases for p2(R).
Compute the matrix [T]% = M1M2M3 using change of basis to get each of the three matrices below.
(You may use a matrix inverse calculator to determine any required inverses of matrices.):
M1 =
M2
M3
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