what is the different of representation of matrix of
a)T(1,x,x^2)={1+x ,3-x^2,4+2x-3x^2}
b)(x,y,z)=(x+y+z,x-y-3z,-x+y+3z)
c){(0,0,1),(1,0,1),(0,0,1)}

Question

what is the different of representation of matrix of
a)T(1,x,x^2)={1+x ,3-x^2,4+2x-3x^2} 
b)(x,y,z)=(x+y+z,x-y-3z,-x+y+3z)
c){(0,0,1),(1,0,1),(0,0,1)}

anonymous · Answer

@TuringTest  help pls

turingtest · Answer

What is the question asking for exactly?

anonymous · Answer

how to represent this matrix are the  the same or different?

turingtest · Answer

well starting with the first one, we should write out what we know$$A\vec x=\vec b$$$$A\left[\begin{matrix}1\x\x^2\end{matrix}\right]=\left[\begin{matrix}1+x\3-x^2\4+2x-3x^2\end{matrix}\right]$$

turingtest · Answer

this tells you that $A$ is going to be a $3\times3$ matrix because the original and final vectors are $3\times1$, now you just need to identify the elements that the matrix needs to have

turingtest · Answer

what must the first row of A be?

turingtest · Answer

$$A_1\vec x=\vec b$$$$\left[\begin{matrix}a_{11}&a_{12}&a_{13}\end{matrix}\right]\left[\begin{matrix}1\x\x^2\end{matrix}\right]=\left[\begin{matrix}1+x\end{matrix}\right]$$

turingtest · Answer

^that is the first row of A
did you try refreshing yet?

anonymous · Answer

we will have this for number a
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