Question 5: 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Note: A negative amount of money signifies the amount withdrawn from the accounts.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.

Which of the following vector spaces consists of vectors which could denote the amount of money deposited individually by Anamika, Subhasis and Shreya in a particular month such that in that month the amount deposited is 0 in both accounts A1 and A2.