Question
Let V = R3 andW = {(x,y, z)|x+y+z = 0} be a subspace of V. Which of the
following pairs of vectors are in the same coset of W in V?
i) (1,3,2) and (2,2,2). ii) (1,1,1) and (3,3,3).
Answer :
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Skip in 10
To solve this problem, we need to check whether each pair of vectors lies in the same coset of the subspace \( W \) in \( V \). ### Subspace \( W \): The subspace \( W \) is defined as \( W = \{(x, y, z) \in \mathbb{R}^3 \mid x + y + z = 0 \} \), meaning that the vectors in \( W \) satisfy the equation \( x + y + z = 0 \). In this context, the coset of a vector \( v \) in \( V \) is defined as the set \( v + W \), where \( v \in V \). Two vectors \( u
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