複選題22.假設控制器 C≡K, K＞0。以下何者正確? (A) 當 1＜K＜2, 閉迴路系統為穩定 (B) 當 K=2, 閉迴路系統有一個極點在虛軸上 (C) 當 2＜K＜4, 閉迴路系統為穩定 (D) 當 K = 4, 閉迴路系統有一對共厄極點 (E) 當 K ＞ 4, 閉迴路系統有一個不穩定極點

複選題

22.假設控制器 C≡K, K＞0。以下何者正確?
(A) 當 1＜K＜2, 閉迴路系統為穩定
(B) 當 K=2, 閉迴路系統有一個極點在虛軸上
(C) 當 2＜K＜4, 閉迴路系統為穩定
(D) 當 K = 4, 閉迴路系統有一對共厄極點
(E) 當 K ＞ 4, 閉迴路系統有一個不穩定極點

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1. 題目解析題目中提到的回控制系統是...

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2. The linear combination of a set of vectors is an essential element in linear algebra. We say a set V is invariant under linear combination if the implication "∀n ∈ and any set of vectors {v₁, ..., } ⊂ V ⇒ the set of all linear combinations {c₁v₁ + ... + } ⊂ V" holds. And we say a mapping L defined on a set X is invariant under linear combination if the form of linear combination is unchanged under L, or more precisely the statement ", and any set of vectors {x₁, ..., } ⊂ X, the identity L(c₁x₁ + ... + ) = c₁L(x₁) + ... + holds" is true. Which one of the following statements related to linear combination is false (A)Let S be a subset of a vector space V. Then S is a subspace of V if S is invariant under linear combination. (B) Let {V₁, ..., } be a set of k subspaces of a vector space W and denote span{V₁, ..., } as the set of all linear combinations of the form c₁v₁ + ... + with each vᵢ chosen freely from . Then span{V₁, ..., } is also a subspace of W with dim(span{V₁, ..., }) = dim(V₁) + ... + dim() (C) Let A and B be two matrices and denote C := AB. Then each column of C is a linear combination of all columns of A, and so rank≤ rank is implied. (D) A mapping L between two vector spaces is a linear transformation if and only if it is invariant under linear combination. (E) Let (V, (. ,. )ᵥ) be an inner product space. Then (. , .)ᵥ is invariant under linear combination at either one of its two arguments.

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