91Ó°ÊÓ

Two apples and four bananas cost \(\$ 2.00\) and three apples and five bananas cost \(\$ 2.70\). Find the price of each.

Jessica has a collection of 15 coins consisting of nickels, dimes and quarters. If the total worth of the coins is \(\$ 1.80\), how many are there of each? Find all three solutions.

Why is it necessary that a matrix be a square matrix for its inverse to exist? Explain by relating the matrix to a system of equations.

Given the internal consumption matrix \(A,\) and the external demand matrix \(D\) as follows. $$ A=\left[\begin{array}{ccc} .05 & .10 & .10 \\ .10 & .15 & .05 \\ .05 & .20 & .20 \end{array}\right] D=\left[\begin{array}{c} 50 \\ 100 \\ 80 \end{array}\right] $$ Solve the system using the open model: \(X=\mathrm{AX}+D\) or \(X=(I-A)^{-1} D\)