n set of prime numbers P 2ℙ2​, find the​ change-of-coordinates matrix from the basis Upper B equals StartSet 1 minus 2 t plus t squared comma 3 minus 5 t plus 4 t squared comma 2 minus 2 t plus 5 t squared EndSetB=1−2t+t2,3−5t+4t2,2−2t+5t2 to the standard basis Upper C equals StartSet 1 comma t comma t squared EndSetC=1,t, t2. Then find the B​-coordinate vector for negative 6 plus 10 t minus 7 t squared−6+10t−7t2. In set of prime numbers P 2ℙ2​, find the​ change-of-coordinates matrix from the basis Upper B equals StartSet 1 minus 2 t plus t squared comma 3 minus 5 t plus 4 t squared comma 2 minus 2 t plus 5 t squared EndSetB=1−2t+t2,3−5t+4t2,2−2t+5t2 to the standard basis Upper C equals StartSet 1 comma t comma t squared EndSetC=1,t, t2.