need help with questions 3&4. full solutions required, thanks.
ust be given in the final answer of an application, where applicable 1. Determine the polynomial whose graph passes through the points (6, 20), (12, 95), and (-3,-5/2) 2. A square matrix A is said to be idempotent if A2 - A. Prove that if A is idempotent, then 24-I is invertible and is its own inverse. 3. Write the system of linear equations below in the form Ax- b. Then find A-1 and use it to solve for x. y+2z =-3 -x + 2z = 2 x+y, + z = 5 Prove that if S = {ã2, ,, } is a basis for a vector space V, then every vector in V can be written in a unique way as a linear combination of vectors in S 5. a. Find the area of the parallelogram that has the vectors as adjacent sides b. Suppose (i.v)- 2u+3usy', represents an inner product on R. For i (2,1,-3) and v (-1,0,4), Find the distance between u and v . i) Find the projection of v onto iu.
