複選題3、Let U and V be subspaces of Rn and T be a linear transformation from Rn to Rm. Which of the following sets is/are subspace(s) of Rn?(A) {a + b ∈ Rn : a ∈ U and b ∈ V}. (B) {a ∈ Rn : a ∈ U or a ∈ V}. (C) {a ∈ Rn : a ∈ U and a ∈ V}. (D) {a ∈ Rn : T(a) = 0}. (E) None of the above is true.

複選題

3、Let U and V be subspaces of Rⁿ and T be a linear transformation from Rⁿ to R^m. Which of the following sets is/are subspace(s) of Rⁿ?
(A) {a + b ∈ Rⁿ : a ∈ U and b ∈ V}.
(B) {a ∈ Rⁿ : a ∈ U or a ∈ V}.
(C) {a ∈ Rⁿ : a ∈ U and a ∈ V}.
(D) {a ∈ Rⁿ : T(a) = 0}.
(E) None of the above is true.

答案：登入後查看
統計： 尚無統計資料

詳解 (共 1 筆)

MoAI - 您的AI助手

B1 · 2025/09/28

#6805170

1. 題目解析題目要求我們判斷哪些集...

(共 1546 字，隱藏中）

前往觀看

複選題8、Let V together with the inner product (•, •) v be an inner product space over R. For acollection of N linearly independent vectors {w1, ..., wN} in V, let M = [mi，,j] ∈RN✖ Nbethe corresponding Gram matrix, i.e., the (i, j)-th entry of M is given by m{i，,j} = (wi, wj)V.Define the following set of real-valued functions f: V→Rwhich is a vector space over R when combined with standard addition and scalar multiplica-tion of real-valued functions. For anyin the vector space F, defineWhich of the following statements is/are true?(A) M is positive definite.(B) If m1,1 = 2, m2,2 = 1, and m1,2 = -, then ||w1 - w2||V = 4, where ||\cdot||_V is the vector norm induced by the inner product(•, •) v.(C) (f, g)F is an inner product for elements f, g∈ F.(D) Given g(y) = (v1, y)V, we have (f, g)F = f(w1) for all f∈ F.(E) None of the above is true.

詳解 (共 1 筆)

相關試題

相關試卷