المصدر: محتاجه اجابة سريعه لهادي الاسئلة اليوم ولكم جزيل الشكر في منتدى : قسم الرياضيات السؤال الأول Let v1 ,v2 and v3 be vectors in a vector space V and T:V→R³ linear transformation for which T(v1) =(1,-1,3) T(v2)=(0,3,2) T(v3)=(-3,1,2) Show that if {v1,v2} is linearly independent and v3 does not lie in span{v1,v2} then {v1,v2,v3} is linearly independent ====================================================== السؤال الثاني: If T:V3(R)→V3(R) is defined as T(α,β,γ)={α+5β+2γ, α+2β+γ,-α+β} Prove T is linear transformation ======================================================= السؤال الثالث: If {u,v,w} is linearly independent over K-space V Prove that {u+v-3w , u+3v-w ,v+w}is linearly dependent over K ====================================================== سامحوني على هالغلبة بس محتجاهم ضروري جداً
sorry mona i was hery up so i try to give you the solution one by one first for Q1 : v1 = i - j + 3k v2 = 3j + 2k so we do the inner prodect: i
