Question

Let T:R^3>R^2 be the linear transformation given by the rule

T(x1,x2,x3) = (x1-x3, x2+x3)

Find the matrix A that represents T relative to the ordered bases
B={(1,1,1),(1,1,0),(1,0,0)}
and
B'={(1,0),(1,1)}
of R^3 and R^2 respectively

Answer 1

\[T(1, 1, 1) = (1 - 1, 1 + 1) = (0, 2)\]\[T(1, 1, 0) = (1 - 0, 1 + 0) = (1, 1)\]\[T(1, 0, 0) = (1 - 0, 0 + 0) = (1, 0)\]
\[(0, 2) = (-2)\cdot(1, 0) + (2)\cdot(1, 1)\]\[(1, 1) = (0)\cdot(1, 0) + (1)\cdot(1, 1)\]\[(1, 0) = (1)\cdot(1, 0) + (0)\cdot(1, 1)\]
\[A_B^{B'} = \left[\begin{matrix}-2 & 0 & 1 \\ 2 & 1 & 0\end{matrix}\right]\]

Answer 2

thank you so so much

Answer 3

could you answer my other question please alchemista?