Write Syed Mohi on the top of every PageNeeded to be solved correctly in 1 hour in the order to get positive feedback please show me neat and clean work for it by hand solution neededPlease answer should be ? percent perfect please Given P₂ = { a+at+at² | ª, ª, a are reals }B = {1-1², t+t², 2-t-t²} and E= {1, t, 1²}[1] Show that {1-t², t+t², 2-t-t²} are linearly independent. Show all support work.[2] Find the change-of-coordinate matrix from & to B PE-B▲ write all entries in exact form, show support work.[3] Find the E-coordinates of q(t) given that [9]B 2 using change-coordinate-matrix.-131Show work to justify your answer.[4] Find the B-coordinates of p(t) = -4+t+t² using change-coordinate-matrix.Show work to justify your answer.

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Given P₂={a+at+a₂t² B = {1-t², t+t², 2-t-t²} and E= {1, t, t²} [1] Show that {1-12, t+t², 2-t-t²} are linearly independent. Show all support work. | a, ª, a are reals } [2] Find the change-of-coordinate matrix from E to B PE-B ▲ write all entries in exact form, show support work. [3] Find the E-coordinates of q(t) given that [4]B = 2 using change-coordinate-matrix. -3 3 Show work to justify your answer.