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S = {<3, -2, 1, -4>, <2, 1, -2, -2>, <0, -7, 8, -2>} Determine whether...

S = {<3, -2, 1, -4>, <2, 1, -2, -2>, <0, -7, 8, -2>}

Determine whether b = < -4, 12, -12, 8 > is in the span of S. Please write out the vector equation by definition of span. Then convert the vector equation into system of linear equations and matrix equation. No need to solve the equation.

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Answer #1

if b is the span of S then we can write b in the form of linear combination of Vector in S and which is Unique. Here we can see that this linear combination is not unique. Hence b is not a span of S

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