Friday, 13 July 2018

linear algebra - Two vectors are linearly independent?

Let x,y,z be vectors in vector space V. Suppose zL(x,y)
, where L(x,y) is the linear span of x,y.

Show that x,y are linearly independent iff x+z, y+z are linearly independent.

I can easily show that x,y are linearly independent implies linear independence of x+z,y+z. But I have a trouble with showing converse!. I want someone who help me~~

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