Spencer Morrison
09/04/2024 · Senior High School
a) Is the following set of vectors in \( \mathbb{R}^{4} \) linearly dependent, if yes, write the first vector as a linear combination of the other vectors. \( S=\{(1,2,-3,1),(3,7,1,-2),(1,3,7,-4)\} \).
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The set of vectors \( S=\{(1,2,-3,1),(3,7,1,-2),(1,3,7,-4)\} \) in \( \mathbb{R}^{4} \) is linearly dependent. The first vector can be expressed as a linear combination of the other two vectors as \( (1,2,-3,1) = -\frac{1}{2}(3,7,1,-2) + \frac{1}{2}(1,3,7,-4) \).
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