Let v1=[1    0   -2] , v2 = [-2   1    7] , and y= [h   -3   -5]. For what value(s) of h is y in the plane generated by v1 and v2 ? Please help me as soon as possible.

Expert Answers

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y is in the plane if the 3 vectors are linearly dependant.

iff their determinant is 0

A=`det([[1,-2,h],[0,1,-3],[-2,7,-5]])` =0

iff `A=det([[1,-2,h],[0,1,-3],[0,3,-5+2h]])` =0

A=`det([[1,-3],[3,-5+2h]])=-5+2h+9=2h+4` =0


Answer h=-2

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