Answer to Question #44544 in Linear Algebra for JASHVINDER

Question

a) Obtain the solution set of the system x – 3y + 4z = 9, 4x + 3y + 2z = 7, y – 2x = 5 – 10z by
elimination.
b) Express the following problem situation as a linear system, and then solve it by substitution. Also
show the linear system geometrically.
A manufacturer produces two types of cupboards – deluxe and regular. Each deluxe cupboard
requires 12 worker hours to cut and assemble, and 5 worker hours to finish. Each regular
cupboard requires 8 worker hours to cut and assemble, and 3 hours to finish. On a daily basis,
the manufacturer has available 440 worker hours for cutting and assembling, and 175 worker
hours for finishing. How many cupboards of each type should be produced so that all the work
power is utilized?


c) Write the systems obtained in a) and (b) in matrix form.