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If u,v and w is a linearly independent s...

If u,v and w is a linearly independent system of vectors, examine the system p,q and r, where `p=(cosa)u+(cosb)v+(cosc)w` `q=(sina)u+(sinb)v+(sinc)w` `r=sin(x+a)u+sin(x+b)v+sin(x+c)w` for linearly dependent.

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To determine whether the vectors \( p, q, \) and \( r \) are linearly dependent given that \( u, v, \) and \( w \) are linearly independent, we will analyze the linear combination of these vectors. ### Step-by-Step Solution: 1. **Define the Vectors**: We have: \[ p = \cos a \cdot u + \cos b \cdot v + \cos c \cdot w ...
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