The question asls:Show that the range of the linear operator defined by the equations:(adsbygoogle = window.adsbygoogle || []).push({});

W_1=x_1 - 2*x_2 + x_3

W_2=5*x_1-x_2+3 *x_3

W_3=4*x_1+x_2+2*x_3

is not all of R^3, and find a vector that is not in the range.

Well, we know T

T=[1,-2,1;5,-1,3;4,1,2]

I augment W

and we get

T|W=[1,-2,1,W_1;5,-1,3,W_2;4,1,2,W_3]

I do Reduce Echelon

I get zeros on the bottom

so i get

w_1-W_2+W_3=0

k, well, i chose a vector point, (10,5,6)

i get

10 != -1

not sure if this is correct way of solving it.

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# Homework Help: Not sure how to solve this problem ( lin alg.)

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