M and N be subspaces of a vector space V. Consider the following subsets of V. Mn N. (A vector v belongs to MnN if it belongs to both M and N.) MUN. (A vector v belongs to MUN if it belongs to either M or N.) M + N. (A vector v belongs to M + N if there are vectors m€ M and n N such that v= m + n.) MN. (A vector v belongs to M - N if there are vectors me M and n E N such that v mn.) = Which of (a)-(d) are subspaces of V? Answer:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let M and N be subspaces of a vector space V. Consider the following subsets of V.
(a) Mn N. (A vector v belongs to MnN if it belongs to both M and N.)
(b) MUN. (A vector v belongs to MUN if it belongs to either M or N.)
(c) M+N. (A vector v belongs to M+N if there are vectors m€ M and n N such
that v = m + n.)
(d) M - N. (A vector v belongs to M - N if there are vectors m € M and n € N such
that v = m - n.)
Which of (a)-(d) are subspaces of V?
Answer:
Transcribed Image Text:Let M and N be subspaces of a vector space V. Consider the following subsets of V. (a) Mn N. (A vector v belongs to MnN if it belongs to both M and N.) (b) MUN. (A vector v belongs to MUN if it belongs to either M or N.) (c) M+N. (A vector v belongs to M+N if there are vectors m€ M and n N such that v = m + n.) (d) M - N. (A vector v belongs to M - N if there are vectors m € M and n € N such that v = m - n.) Which of (a)-(d) are subspaces of V? Answer:
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