5. Låt T : R* –→ R* ges av att (a, b, c, d) (2a, b+ c,b+c, 2d). (a) Visa att T är en linjär avbildning. (b) Bestäm matrisen för T (i standardbasen). (c) Är T inverterbar? (d) Bestäm om det finns en vektor v +0 vars bild under T är nollvektorn. Om det inte finns en sådan vektor motivera detta.

5. Låt T : R* –→ R* ges av att (a, b, c, d) (2a, b+ c,b+c, 2d). (a) Visa att T är en linjär avbildning. (b) Bestäm matrisen för T (i standardbasen). (c) Är T inverterbar? (d) Bestäm om det finns en vektor v +0 vars bild under T är nollvektorn. Om det inte finns en sådan vektor motivera detta.

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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