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A hardware shop sells screws, bolts and nuts in boxes…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A hardware shop sells screws, bolts and nuts in boxes. Three orders are: $2$ boxes of screws, $2$ of bolts and $3$ of nuts for $130$ rupees; $2$ , $1$ and $4$ for $110$ rupees; $3$ , $3$ and $4$ for $190$ rupees. The inverse of the coefficient matrix is $

\displaystyle \begin{bmatrix} -8 & 1 & 5 \\ 4 & -1 & -2 \\ 3 & 0 & -2 \end{bmatrix}

$. Find the price of a box of each.

Need a reminder? The key ideaShow

$AX = B$ has the unique solution $X = A^{-1}B$ when $|A| \ne 0$ . When $|A| = 0$ there is no solution or infinitely many. A homogeneous system $AX = O$ has a non-zero solution exactly when $|A| = 0$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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