Question

g Problem 13. (1.4 points) Which of the following statement is TRUE regarding the dimensionality of the subspace W. (A) It can be shown that W = {p(x) ∈ P2 : x dp dx(x) = p(x)} is a subspace of the vector space P2, and the dimension of W is 2. (B) It can be shown that W = A ∈ M2×2 : AB = BA, where B = 1 1 0 1 is a subspace of the vector space M2×2, and the dimension of W is 2. (C) It can be shown that W = x y z ∈ R 3 : x + 2y − 4z = 0 and y − 3z = 0 is a subspace of the vector space R 3 , and the dimension of W is 2. (D) It can be shown that W = A ∈ M2×2 : A T = A is a subspace of the vector space M2×2, and the dimension of W is 2. (E) It can be shown that W = {p(x) ∈ P2 : p(1) = 0} is a subspace of mathcalP2, and the dimension of W is 1.

Answer 1

Answer: (C) It can be shown that W = x y z ∈ R 3 : x + 2y − 4z = 0 and y − 3z = 0 is a subspace of the vector space R 3 , and the dimension of W is 2.

Step-by-step explanation: