Question 2: (4 marks) Given set S is a subspace of P2, find a basis for...
Find a basis of the following subspace W of P2 and find the dimension of W. You do not have to show that W is a subspace of P2. W = {p € P2 | p' (1) = 0}
Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W! Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W!
2. (4) Determine if each of the following is a subspace of P2[x] (the set of all polynomials of degree no more than 2). (a) All polynomials in P2[x] that satisfy f(1) = f(0) + 1; (b) All polynomials in P2 [x] that satisfy f(2x) = f(-x). (Hint: use the condition to find an equation of the coefficients of the polynomial f(x).)
Please refer to illustration for question. The given set is a basis for a subspace W. Use the Gram-Schmidt process an orthogonal basis for W. 1 0 Let x1 = , X2 = , X3 = 1 1
Find a basis for the subspace of R3 spanned by S. S = {(4, 4, 9), (1, 1, 3), (1, 1, 1)} STEP 1: Find the reduced row-echelon form of the matrix whose rows are the vectors in S. 1 0 0 1 0 0 0 x STEP 2: Determine a basis that spans S. 35E
Use the solution method from this example to find a basis for the given subspace. 1 4 0 5 1 S = span -1 0 -1 4 0 5 Give the dimension of the basis.
3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30 B. The set of all (x1,22, z3, z4) that satisfy both 5x1+22 3 0 3. Is each of the following is a subspace of R4? If yes, find a basis A. The set of all (x1, z2, s, z4) that satisfy both 2x1-32 o 51 +22 30...
Find a vector v-0such that the set 0 0 is a basis of the subspace
Find a basis of the following subspace W of P, and find the dimension of W. You do not have to show that W is a subspace of P2. W = {P € P2 | p' (1) = 0}
Prob. 4 (12.5 pts) The set of vectors S = {p1.p2.p3 } may be a basis for P2 p1 = 1 + x + x2 p2 = x + x2 p = x² a) Verify that this is the case. b) If it is a basis, find the coordinate vector of b relative to S. b = 7 - x + 2 x2