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2. Let T: R³ → R² be given by (E)- 3x1 + 2x2 4.x2 – 5x3 T = and let L: R → R³ be given by 6x1 + 12 -3x2 L (a) Show that T and L are linear transformations by showing that they are given by matrix multiplication. (b) Find the standard matrix for the composition LoT.

2. Let T: R³ → R² be given by (E)- 3x1 + 2x2 4.x2 – 5x3 T = and let L: R → R³ be given by 6x1 + 12 -3x2 L (a) Show that T and L are linear transformations by showing that they are given by matrix multiplication. (b) Find the standard matrix for the composition LoT.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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2. Let T: R³ → R² be given by 3x1 + 2x2 4.x2 – 5x3 T I2 and let L: R² → R³ be given by (:)- 6x1 + 12 -3.12 (a) Show that T and L are linear transformations by showing that they are given by matrix multiplication. (b) Find the standard matrix for the composition Lo T.
Transcribed Image Text:2. Let T: R³ → R² be given by 3x1 + 2x2 4.x2 – 5x3 T I2 and let L: R² → R³ be given by (:)- 6x1 + 12 -3.12 (a) Show that T and L are linear transformations by showing that they are given by matrix multiplication. (b) Find the standard matrix for the composition Lo T.
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