4) Show that the subspaces of R? are precisely {0}, R2, and all lines in R? through the origin.

Q: rove that W2 = {(a,b) E R² : a = 26²} is not a subspace of R?.

A:

Q: 3. Determine whether the given set is a subspace of M2x2 with real entries. {6 ) la = b}.

A:

Q: Let B = {(1,2,3), (3, 2, 1), (0, 0, 1)}. Show that B is linearly independent and spans R3. Show all…

A:

Q: Šolve the problem. 1) Determine which of the following sets is a subspace of Pn for an appropriate…

A:

Q: Let H = {[ 21 12 x1, x2 € R 1,2 Show whether or not H is a subspace of R3.

A: We satisfy the clouser and scaler multiplication and show that 0 vector is also in H so H is a…

Q: 3. Determine whether X1 W E R? : x² + x2 = | X2 is a subspace of R².

A:

Q: does a basis for a subspace W always span W

A: our objective is to conclude.

Q: Given = 2 2 -6 3 6 1-0 and -6 36 find the closest point to in the subspace W spanned by

A: Given,        To  find the closest point to v in the subspace W spanned by

Q: If S is a subspace of R", then so is the orthogonal complement of S.

A:

Q: Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1,y1)…

A: Given  be the set of all pairs  of real numbers together with the following operations:

Q: . Let L ⊂ R3 be the following subspace: L = {(x1, x2, x3) : x1 + x2 + 3x3 = 0}, and let ℓ be the…

A:

Q: 1 :) Given v = -2 -5 -0 and 2 -16 6 -9 4 -4 0 -6 4 find the closest point to v in the subspace W…

A:

Q: 10. Prove that W₁ {(a₁, a2,..., an) € F": a₁ + a₂ + + an = 0} is a subspace of Fr, but W₂ = {(a1,…

A:

Q: Find bases for the following subspaces of F5: and W₁ = {(a1, 02, 03, 04, 05) € F5: α₁ - 03 - α4 = 0}…

A: Given subspaces areWe have to find the bases for the above subspaces also we have to determine their…

Q: 5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³…

A:

Q: Prove that if U and V are subspaces of R" and U <V then V+<U+.

A:

Q: Determine whether the vectors w₁ = [2,1,–3], w₁ = [4,0,2], and w3 = [2,-1,3] form a basis for the…

A:

Q: Let A = {(1, –2,0), (0,0, 1), (-1, 2,0)}. Determine if A spans R. If A does not span R°, give a…

A: To find wheather A spans R3 we have to check if it forms a basis in R3

Q: [W1 W2 E R3: w1 – 2w2 + 3w3 = 0} is a subspace of W3 %3D 1. Show that the set W = R3.

A:

Q: 6. Is the set of points {(x₁, x2 + 1) |x₁, x₂ € R} a subspace of R²? 7. Is the set of points…

A: Subspace of the vector space