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I have a T/F which I need to prove.

X1, X2, X3 belong to vector-space V.

Y1 = X1 + X2, Y2 = X3.

Span{Y1, Y2} is contained in but not equal to span{X1, X2, X3}.

I am not sure which one it is:

since y-span can be represented as span{X1 + X2, X3} it may be false, but then if all spans are subspaces, these two subspaces are not of the same dimension, i.e. they are not equal, then the statement is true. Obviously one of my reasonings is wrong. :uhh:

Could someone clear up this for me?

Thank you in advance.

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# Equality of spans

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