- 2 Let P2 A Bt Ct A B C Are Scalars Consider The Vectors V1 1 T V2 T T2 And V3 T In P2 And 1 (107.66 KiB) Viewed 30 times
= = 2. Let P2 = {a + bt + ct? | a, b, c are scalars). Consider the vectors V1 = 1- t?, v2 = t + t2 and V3 = t in P2, and let S = {V1, V2, V3}. (a) Suppose that X1, X2, X3 are scalars such that = X1V1 + x2V2 + X3V3 = 0 = [ 12 Write down a system of equations that X1, X2, X3 must satisfy in order for this equation to hold. Use this to find a matrix A for which Ax = 0, where x= (b) What must be true about the matrix A from part (a) in order for S to be linearly independent? Explain why. Use your criterion to verify whether S is linearly dependent or independent. (C) For this problem suppose that S is linearly independent (whether it is true or not). Is it also true that S is a basis of P2? Explain why/why not?