第一次习题è®&um

X l1 2 lg2 x l1 2 f3 x w1 w2 2

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 间 是 L(β , S), 则 已 知 α ∈ S 但 α ∈ / L(β , S),故可以设 α = k β + γ ,其中,γ ∈ S,且可知 k = 0。 因此,β = 1 α − 1 γ ∈ L(α, S)。证毕。 k k Exercise 6 设 W, W1 , W2 都是线性空间 V 的子空间,其中 W1 ⊆ W2 , 且 W ∩ W1 = W ∩ W2 ,W + W1 = W + W2 。试证明 W1 = W2 。 证明 1: 只需证 W2 ⊆ W1 ,即证:∀α ∈ W2 都有 α ∈ W1 。 已知 W + W1 = W + W2 ,则可知存在 β ∈ W1 , γ ∈ W ,使得 α = β + γ 。 又已知 W1 ⊆ W2 ,故 β ∈ W2 。从而,有 α − β = γ ∈ W ∩ W2 。 再由已知 W ∩ W1 = W ∩ W2 得 α − β ∈ W ∩ W1 ⊆ W1 ,从而 α ∈ W1 。...
View Full Document

This note was uploaded on 03/25/2010 for the course MATH 40 taught by Professor F.yu during the Spring '05 term at Tsinghua University.

Ask a homework question - tutors are online