Proof When the set of vectors {u1, u2, . . . , un} islinearly independent and the set
Chapter 4, Problem 70(choose chapter or problem)
When the set of vectors \(\left\{\mathbf{u}_{1}, \mathbf{u}_{2}, \ldots ., \mathbf{u}_{n}\right\}\) is linearly independent and the set \(\left\{\mathbf{u}_{1}, \mathbf{u}_{2}, \ldots ., \mathbf{u}_{n}, \mathbf{v}\right\}\) is linearly dependent, prove that v is a linear combination of the \(\mathbf{u}_{i}\)’s.
Text Transcription:
{mathbf u_1, mathbf u_2, ldots ., mathbf u_n}
{mathbf u_1, mathbf u_2, ldots ., mathbf u_n, mathbf v}
mathbf u_i
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