[₂] L with respect to each of the given bases. Suppose L: R² → R³ is defined by L [L(u)]B₁ = [L(u)]B₂ = ↓ 1 X₁ + X₂ -{]]]~~-~-{][B][B) and B₂ = -X₁. Let B₁ = be ordered bases for R³. If u = [3]. A find [L(u)], and [L(u)], the coordinate vectors

find the ndraed limil kan 8x'15X 13.

D A ({0},+) B Z₂ ⒸZ₁ x Z6 D E Z₁ Z₂ x Z₂ Which one of the following is isomorphic to Z4 x Z6/((2,4))? ...

Suppose L: R2 R³ is defined by L X1 →>> the given bases. [L(u)]B₁ = [4(u)] B₂ = ↓ → 1 -Q][*3]-{]}---CH:H:}· -X1 Let B₁ = 2, 5, 1 and B₂ 2 0 4 4 - x2 = + x₂ 2X2 = 0 1 2 4 9 8 be ordered bases for R³. If u = 6 3 [³], find [L(u)] and [L(u)], the coordinate vectors of L with respect to each of 4

Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this implies about the coefficients an.

Find of 3xy – x³ = 5 at (1, 2)

Please do 3e and 4a

Show that MnXn and Rn^2 are isomorphic.

-(1-2x) Uy

Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?