Suppose B, X, and A are vectors. Any of the equations below would, if true, demo

Question

Suppose B, X, and A are vectors. Any of the equations below would, if true, demonstrate that set S = {B, X, A) is linearly dependent. However, without additional information we have no reason to believe that any of the equations is actually true. Suppose that, in addition, we know that A = 5 B - 2 X. With this additional information, which, if any, of the equations must be true and therefore be valid expressions of the linear dependence of the set S? 3B + 3X - 9A = 0 5B - 2X + A = 0 -3 B + X + 2A = 0 -15B + 6X + 3A = 0 10B - 25X + 5 A = 0 None of these

Explanation / Answer

So, we have A = 5B -2X which proves A, B and X are linearly dependent

we need to check that the given options must be derived from above equation by multipling the

equation by a constant.

Option 1 and 2 does not convert to original equation

If we multiply above equation by 3 and rearrange we get : 3A -15B +6X =0.This is true

If we multiply above equation by 5 and rearrange we get : 5A = 25B -10X ---> 10X -25B +5A =0. This does not match with any option.

So, Option 4 : 3A -15B +6X =0

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