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## Homework Statement

Determine whether the following vectors are linearly independent in P

_{3}"not sure what P

_{3}stands for maybe polynomial of third degree?"

1,x

^{2},x

^{2}-2

let p

_{1}(x)=1

p

_{2}(X)=x

^{2}

p

_{3}=x

^{2}-2

c

_{1}p

_{1}(x)+c

_{2}p

_{2}(x)+c

_{3}p

_{3}(x)=z

where z=0x

^{2}+0x+0

I then create a matrix using the above relation where I get

(c

_{2}+c

_{3)x2+}c

_{1}-2c

_{3}

The matrix i'm thinking if solving looks like this [0 1 1;0 0 0; 1 0 -2] I know the zero must be at the bottom so I switch things up and get [1 0 -2; 0 1 1;0 0 0]

When I actually solve it I get c

_{2}=-c

_{3}

which is a nontrivial solution, so I state that it is linearly dependent.

Is my work correct, and or is there a faster way to come up with the conclusion that it is linearly dependent?

Thanks