Question: math Algebra Suppose { V1, v2, v3} is a linearly independent set of vectors in R3 and let w = ajV1 + a2v2 + 03V3,

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Algebra Suppose { V1, v2, v3} is a linearly independent set of vectors in R3 and let w = ajV1 + a2v2 + 03V3, with real numbers a1, a2, a3, be a linear combination of these vectors. Prove the following statement: The vectors w, v2, v3 are linearly independent if, and only if, al * 0. Hint: To show one implication, assume 0 = 1W +12V2+13V3 for some numbers 21, 12, 23, and use that V1, V2, V3 are linearly independent to derive that all r's must be zero

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