Question

can u please help with linear transformations?

Answer 1

use the definition of a linear transformation to show that the function
\[T:R ^ { 3 }\rightarrow R ^{2}\]
given by the formula
\[T(x _{1},x _{2},x _{3}) = (2x _{1}-x _{2}+x _{3},x _{2}-4x _{3})\]
is a linear transformation

Answer 2

\[ T(x _{1} ,x _{2},x _{3}) = (2x _{1}-x _{2}+x _{3},x _{2}-4x _{3})\]
your variables are
\[ (x_1, x_2, x_3) \text{change it to }\; c(x_1, x_2, x_3) + d(y_1, y_2, y_3)\\
= (cx_1 + dy_1, cx_2 + dy_2,cx_3 + dy_3) \]

try to transform this and see what you get.