Let T be a linear transformation from R² to R³ and suppose that (Q)-[]). T ¹ ([³]) - the vector [-2.] 5 3 and T as a linear combination of vectors [3] and [A] Show your

Determine whether or not →v = (3, 9, −4, −2) ∈ R^4 is a linear combination of →u1 = (1, −2, 0, 3), →u2 = (2, 3, 0,−1), and →u3 = (2, −1, 2, 1), i.e., whether or not →v ∈ span (→u1, →u2, →u3).

Prove that Mobius transformation can have at most two fixed points

Calculate 121x dxdy where R is the parallelogram with vertices (0,0), (6,2), (7,6) R 1 -(v — Зи), у 11 -(4v – u) 11 and (1,4) using the transformation x =

Find the bilinear transformation which maps the points (-1,0,1) into points (0,i,3i)

Let ℝ [x]≤ 2 ---> ℝ be a linear transformation such that T(x2)= -3, T(x2+x)=-4, T(x+1)=-1 What is T(ax2+bx+c) for orbitrary a,b,c ∊ℝ?

QI) Write down the transformation T (B} 2, 2, (4} 2

Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is linearly independent. If yes, show work, if no state a linear combination among the vectors of the list that adds up to a vector in the list. I am having trouble grasping the concept so if anyone can explain this problem I'd appreciate it.

Explain an example of vector space.

Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain clearl