There are three kinds of liquids X, Y, Z. Thr | vedclass

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(B) Let $x_n, y_n, z_n$ be the amounts of liquids $X, Y, Z$ in jar $J_1$ after $n$ operations.Initially,$J_1$ contains $100 \, ml$ of $X$,$J_2$ contai

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$x > z > y$

Vedclass · Answer

(B) Let $x_n, y_n, z_n$ be the amounts of liquids $X, Y, Z$ in jar $J_1$ after $n$ operations.Initially,$J_1$ contains $100 \, ml$ of $X$,$J_2$ contains $100 \, ml$ of $Y$,and $J_3$ contains $100 \, ml$ of $Z$.After one operation,the composition of $J_1$ changes as liquid is transferred out and back in.Let $A_n$ be the state vector representing the amounts of $X, Y, Z$ in the jars. The process is a linear transformation.After $n=4$ operations,the amount of $X$ remains the largest because it started in $J_1$ and is only partially removed and partially returned.The amount of $Z$ in $J_1$ increases as it is transferred from $J_3$ to $J_1$ in the third step of each operation.The amount of $Y$ in $J_1$ is the smallest as it must travel through $J_2$ and $J_3$ before reaching $J_1$.Thus,the amounts in $J_1$ satisfy $x > z > y$.

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