E is a vec torial space which has as base B=(i^→ ,j^→ ,k^→ ). f: E→E is a linear application such that f(i^→ )=−i^→ +2k^→ ; f(j^→ )=j^→ +2k^→ and j(k^→ )=2i^→ +2j^→ . 1. Write the matrix of f in base B. 2. Show that the kernel (ker f) of f is a straigh line; give one base of its. 3.Determinate Im f.


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 134009 by mathocean1 last updated on 26/Feb/21

$E i s a v e c t o r i a l s p a c e w h i c h h a s a s$ $b a s e B = (\vec{i}, \vec{j}, \vec{k}) . f : E \to E i s a l i n e a r$ $a p p l i c a t i o n s u c h t h a t$ $f (\vec{i}) = - \vec{i} + 2 \vec{k}; f (\vec{j}) = \vec{j} + 2 \vec{k} a n d$ $j (\vec{k}) = 2 \vec{i} + 2 \vec{j} .$ $1 . W r i t e t h e m a t r i x o f f i n b a s e B .$ $2 . S h o w t h a t t h e k e r n e l (k e r f) o f f$ $i s a s t r a i g h l i n e; g i v e o n e b a s e o f i t s .$ $3 . D e t e r m i n a t e I m f .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum