I am looking for examples in my book and can\'t seem to findany. I do not know w

Question

I am looking for examples in my book and can't seem to findany. I do not know where to begin with this problem. The vectors x1=(1,2,2), x2=(2,5,4), x3=(1,3,2), x4=(2,7,4),x5=(1,1,0) (these vectors are transposed). span R^3. Paredown the set {x1,x2,x3,x4,x5}to form a basis for R^3. I someone can show me how to set this up I will rateASAP. I am looking for examples in my book and can't seem to findany. I do not know where to begin with this problem. The vectors x1=(1,2,2), x2=(2,5,4), x3=(1,3,2), x4=(2,7,4),x5=(1,1,0) (these vectors are transposed). span R^3. Paredown the set {x1,x2,x3,x4,x5}to form a basis for R^3. I someone can show me how to set this up I will rateASAP.

Explanation / Answer

Procedure: Put the five vectors in a matrix, if you want to get a base, youhave to get the ones that are linearly independent. Say, youneed three vectors, whose combination can make the 5. So put the matrix     x1     x2     x3     x4     x5 and perform elementary operations until getting three vectors, anythree vectors is a base, just get three and thats it. I mean, maketwo of the rows 0.

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