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Consider the set S = {<1,-1,-2> , <a,0,-a> , <1,1,a-2>} For which...

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masterpiece11 | Student | (Level 1) Salutatorian

Posted April 1, 2013 at 4:03 AM via web

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Consider the set S = {<1,-1,-2> , <a,0,-a> , <1,1,a-2>}

For which values of "a" would S be a basis for R^3 ?

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 1, 2013 at 8:20 AM (Answer #1)

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Let us check if given vectors are Linearly independent

Let for some scalar x,y, and z

`x[1,1,-2]+y[a,0,-a]+z[1,1,a-2]=[0,0,0]`

``   `[[1,a,1],[1,0,-a],[-2,-a,a-2]][[x],[y],[z]]=[[0],[0],[0]]`

The rank of the cofficient matrix is 3 if  

so vectors [1,1,-2],[a,0,-a],[1,1,a-2] are linearly independent if `a!=0,-2`.

It will be form  basis of the  S. 

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