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how to show that if B={u1,u2,u3,u4} where u4 is a linear comb. of its preceeding vectors then B is linearly dependent??

Mathematics
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u4 is a linear combo of u1, u2, and u3, so there are constants a, b, c (not all zero) such that u4 = a*u1 + b*u2 + c*u3. That means that a*u1 + b*u2 + c*u3 + (-1)u4 = 0. So we have a nontrivial linear combination of the u's that add to 0. This means that the vectors are linearly dependent. So the matrix that includes those vectors as column vectors is linearly dependent by definition.

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