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Speak With a Friendly Mentor. ###### Vaishnavi Mishra posted an Question
April 18, 2021 • 07:21 am 30 points
• IIT JAM
• Mathematics (MA)

# Addition and scalar multiplication for cosets if w is a subspace of the vector space v(f), then the addition and scalar multiplication of cosets in v/w are defi

Addition and Scalar multiplication for cosets If w is a subspace of the vector space V(F), then the addition and scalar multiplication of cosets in V/W are defined as follows (W+ a)+ (W + B) = W + (a + B),v a, B e V a(W+ a) = W + (aa) Vae F Theorem If WV is a subspace of vector space V(F), then the set VW of all cosets of W in V

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• ##### Alka gupta

yes, definition of cosets is absolutely correct when we multiply a scalar by coset element then we get a (W + b) = aW +ab = W +ab because aW =W

why aw =w

W is a subspace when we operate it by any scalar then we get again same subspace...

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