Mathematics
OpenStudy (anonymous):

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

OpenStudy (anonymous):

$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)$ $A_B^{B'} = \left[\begin{matrix}-2 & 0 & 1 \\ 2 & 1 & 0\end{matrix}\right]$

OpenStudy (anonymous):

thank you so so much

OpenStudy (anonymous):