Скачать или смотреть Linear Algebra Example Problems - Linear Combination of Vectors #1

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Given the vectors v1, v2, and v3, we see if the vector b can be written as a linear combination of the vectors.

This can be easily determined by constructing an augmented matrix, performing row operations, and finding the coefficients such that a1*v1 + a2*v2 + a3*v3 = b.

If values for a1, a2, and a3 can be found, then b is a linear combination of {v1,v2,v3} and we say that b is in the Span{v1,v2,v3}. If the augmented matrix has no solution, then b is NOT a linear combination of the vectors.

For this example, b CAN be written as a linear combination.

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