Question

T:R3 -> R2 is a linear transformation where T(1,1,2)=(2,3) T(1,0,1)=(1,1) and T(1,1,0)=(2,1) Determine T(X,Y,Z) and prove that T(X,Y,Z) is a linear transformation.

Answer 1

\[A\begin{bmatrix}1\\1\\2\end{bmatrix}=\begin{bmatrix}2\\3\end{bmatrix}; A\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}1\\1\end{bmatrix};
A\begin{bmatrix}1\\1\\0\end{bmatrix}=\begin{bmatrix}2\\1\end{bmatrix}\]
If you let
\[A=\begin{bmatrix}a_{11}&a_{12}&a_{13}\\
a_{21}&a_{22}&a_{23}\\
\end{bmatrix}\]
Then you will get two system of equations so that you can solve for the entries of A.

Answer 2

I don't quite understand. Could you please explain?

Answer 3

put the following matrix into rref

\[\left[\begin{array}{ccccc} 1 & 1 & 2 & 2 & 3 \\ 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 2 & 1 \\ \end{array}\right]\]

Answer 4

On it.

Answer 5

Could you tell me what for, please?

Answer 6

it is a way of finding the answer...it will give you what

T(1,0,0)
T(0,1,0) and T(0,0,1) are

Answer 7

then T(x,y,z)=xT(1,0,0)+yT(0,1,0)+zT(0,0,1)

Answer 8

Is this correct ?