3) Let T: R' R' be a linear transformation and X x2 T(x) is defined as X3 follows: T(x1,x2,x3) = (4.x1 – x2 +2x3, 3x1 +2x2 -5x3, 2x +x2 - X3) a) Find the standard matrix of T. b) Show that T is invertible by row reducing the appropriate matrix, and find the inverse of the standard matrix. c) Find a formula for T. T-v)= b. Give the equivalent

3) Let T: R' R' be a linear transformation and X x2 T(x) is defined as X3 follows: T(x1,x2,x3) = (4.x1 – x2 +2x3, 3x1 +2x2 -5x3, 2x +x2 - X3) a) Find the standard matrix of T. b) Show that T is invertible by row reducing the appropriate matrix, and find the inverse of the standard matrix. c) Find a formula for T. T-v)= b. Give the equivalent

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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Question

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3) Let T: R» R' be a linear transformation and X = x)
T(x)is defined as
[x3
follows:
T(x1,x2, x3) = (4x| – x2 + 2x3, 3x¡ + 2x½ - 5x3, 2x + x2 – x3)
a) Find the standard matrix of T.
b) Show that T is invertible by row reducing the appropriate matrix, and find the inverse
of the standard matrix.
c) Find a formula for T.
d) Suppose a y e R' and a bɛ R' such that T'(y)= b. Give the equivalent
statement relating b,T, and y.

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