Question 6: Anamika, Subhasis, and Shreya deposit x, y, and z amount …

Anamika, Subhasis, and Shreya deposit $x, y,$ and $z$ amount of money (in thousands) respectively, every month in two different accounts $A_1$ and $A_2$. The amount of money is distributed in these two accounts $A_1$ and $A_2$ as $x + y$ and $2y - z$ respectively. This can be thought of as a linear transformation

$T : \mathbb{R}^3 \to \mathbb{R}^2$

defined by

$T(x, y, z) = (x + y, 2y - z)$

Note: A negative amount of money signifies the amount withdrawn from the accounts.

Using the given information, answer the subquestions.