Form a matrix equation to represent the information and use matrix methods to find the price of a physics…

Question

Form a matrix equation to represent the information and use matrix methods to find the price of a physics book and that of a mathematics book.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for questions b) and c) from the image.

Question b) i): Form a matrix equation to represent the information.

Define variables for the prices.
Let $p$ be the price of a physics book and $m$ be the price of a mathematics book.
Write down the equations from the given information.
Okello bought 5 physics books and 6 mathematics books for Ksh 2440:
$5p + 6m = 2440$
Ali bought 7 physics books and 9 mathematics books for Ksh 3560:
$7p + 9m = 3560$
Form the matrix equation.
$\boxed{\begin{bmatrix} 5 & 6 \\ 7 & 9 \end{bmatrix} \begin{bmatrix} p \\ m \end{bmatrix} = \begin{bmatrix} 2440 \\ 3560 \end{bmatrix}}$
Question b) ii): Use matrix methods to find the price of a physics book and that of a mathematics book.
Find the inverse of the coefficient matrix.
Let the coefficient matrix be $A = \begin{bmatrix} 5 & 6 \\ 7 & 9 \end{bmatrix}$ .
The determinant of $A$ is $\det(A) = (5 \times 9) - (6 \times 7) = 45 - 42 = 3$ .
The inverse of

Form a matrix equation to represent the information and use matrix methods to find the price of a physics book and that of a mathematics book.