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Vaishnavi mishra Asked a Question
April 18, 2021 7:21 ampts 30 pts
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 thankyou
    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
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    Vaishnavi mishra
    why aw =w
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