Consider the subspace W p P3 p0 0 pl 0 Find a basis for

Consider the subspace W = {p P3 | p(0) - 0, p(l) = 0}. Find a basis for W and deduce the dimension of W. Problem 2) The matrices A, B are 7 times 7 matrices and ft is a row echelon form for A. Assume that ft has rank 5.

Solution

a.) As the matrix is 7*7 and rank is 5. So, number of 0 rows are 2.

b.) Rank of A = rank of R = 5

c.) Row RB can have maximum 14 0 elements