E is a vectorial plane. his base is B=(i^→ ;j^→ ). f is an endomorphism defined by f(i^→ )=−((√2)/2)i^→ +((√2)/2)j^→ and f(j^→ )=((√2)/2)i^→ −((√2)/2)j^→ 1)Show that ker f is a vectorial straigh line and his base is e_1 ^→ =(√2)i^→ +(√2)j^→ 2)show that G, the set of vectors u^→ ∈ E such as f(u^→ )=(√2)u^→ is a vectorial straigh line and his Base is e_(2 ) ^→ =i^→ +j^→ 3) Determine the matrix A′ of f in B′ if B′=(e_1 ^→ ;e


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 97380 by mathocean1 last updated on 07/Jun/20

$E i s a v e c t o r i a l p l a n e . h i s b a s e i s$ $B = (\vec{i}; \vec{j}) . f i s a n e n d o m o r p h i s m d e f i n e d$ $b y f (\vec{i}) = - \frac{\sqrt{2}}{2} \vec{i} + \frac{\sqrt{2}}{2} \vec{j} a n d f (\vec{j}) = \frac{\sqrt{2}}{2} \vec{i} - \frac{\sqrt{2}}{2} \vec{j}$ $1) S h o w t h a t k e r f i s a v e c t o r i a l s t r a i g h$ $l i n e a n d h i s b a s e i s {\vec{e}}_{1} = \sqrt{2} \vec{i} + \sqrt{2} \vec{j}$ $2) s h o w t h a t G, t h e s e t o f v e c t o r s \vec{u}$ $\in E s u c h a s f (\vec{u}) = \sqrt{2} \vec{u} i s a v e c t o r i a l s t r a i g h$ $l i n e a n d h i s B a s e i s {\vec{e}}_{2} = \vec{i} + \vec{j}$ $3) D e t e r m i n e t h e m a t r i x A^{'} o f f i n$ $B^{'} i f B^{'} = ({\vec{e}}_{1}; {\vec{e}}_{2}) .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum