2.Let T: R³ → R² be given by3x1 + 2x24.x2 – 5x3TI2and 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 matrixmultiplication.(b) Find the standard matrix for the composition Lo T.

Part(a) A mapping T:V→W is a linear transformation if: TaX+bY=aTX+bTY Here, a,b are constants and…

Answered: 2. Let T: R³ → R² be given by (E)- 3x1…

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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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.