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

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 .