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Consider the transformation T: M2x2 - P, defined by = (a + d) + ct + 2br? с а for a, b, c, and d real numbers. Let B = and 6 = {1, t, 12}. (a) For m = 1 find T (m). That is, find T -3 5 (b) Find a basis for the kernel of T. Please show work.

Consider the transformation T: M2x2 - P, defined by = (a + d) + ct + 2br? с а for a, b, c, and d real numbers. Let B = and 6 = {1, t, 12}. (a) For m = 1 find T (m). That is, find T -3 5 (b) Find a basis for the kernel of T. Please show work.

Advanced Engineering Mathematics
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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(c) Let u = and v = . l. Carefully show that Tis a linear transformation by showing: (i) T (u + v) = T (u)+ T (v) (ii) T (xu) = xT (u) (x ER)
Transcribed Image Text:(c) Let u = and v = . l. Carefully show that Tis a linear transformation by showing: (i) T (u + v) = T (u)+ T (v) (ii) T (xu) = xT (u) (x ER)
Consider the transformation T: M2x2 → P, defined by = (a + d) + ct + 2br? с а for a, b, c, and d real numbers. Let B = and 6 = {1, t, 1²}. (a) For m = 1 find T (m). That is, find T -3 5 (b) Find a basis for the kernel of T. Please show work.
Transcribed Image Text:Consider the transformation T: M2x2 → P, defined by = (a + d) + ct + 2br? с а for a, b, c, and d real numbers. Let B = and 6 = {1, t, 1²}. (a) For m = 1 find T (m). That is, find T -3 5 (b) Find a basis for the kernel of T. Please show work.
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