Model and solve problems that involve matrices of beyond dimension 2 × 2, including the solution of systems of linear equations, with technology.

A factory produces three types of electronic components: resistors, capacitors, and inductors. The production constraints are modelled by the following system of linear equations, where x is the number of resistors, y is the number of capacitors, and z is the number of inductors (in thousands of units): 2x + y - z = 15 x - 3y + 2z = 4 3x + 2y + z = 24 Using technology, solve the system to find the production levels x, y, and z.

A manufacturing plant produces three types of circuit boards. The production costs (in dollars per unit) are set up in a system of equations based on three constraints: \(2x + 3y + z = 50\) \(x + 2y + 3z = 44\) \(3x + y + 2z = 50\) where \(x\), \(y\), and \(z\) represent the costs of labour, materials, and overhead respectively. a) Form the augmented matrix for this system of linear equations. (1 mark) b) Use technology to solve the system and determine the values of \(x\), \(y\), and \(z\). (1 mark) c) Verify that your solution from part b) satisfies the second equation. (1 mark)