Linear Algebra Answers

Find the product of the following question.

A=( 1 2 3 4) B = ( 1 2 3

( 5 6 7 8 ) ( 4 5 6

( 7 8 9

( 10 11 12 )

Consider the system of equations

11 2x1 + x2 + 4x3 =

3x1 + x2 + 5x3 =14

A feasible solution is x1 = ,2 x2 = ,3 x3 = .1 Reduce this feasible solution to a basic

feasible solution.

1. Determine P(∅). 2. Determine P({1}). 3. Determine P({1, 2, 3}).  

The Solfel Dynamic Frames creates two kinds of frame, wooden frame and metal frame. Each frame is processed under two machines, M1 and M2. Machine M1 has a maximum of 250 hours to be used per production and machine M2 has a maximum of 200 hours. Each wooden frame requires 2 hours to be processed in M1 and 2.5 hours in M2. Each metal frame requires 1.5 hours in M1 and 1 hour in M2. Profit is P 500 for a wooden frame and P 400 for a metal frame. Determine the number of wooden frame and metal frame to be produced to obtain a maximum profit if wooden frame must not exceed 20 pcs for each production. 

Find the conditions on a, b, and c so that the following linear system of equations have a solution.

x + 2y − 3z = a

2x + 6y − 11z = b

2x − 4y + 14z = 2c

Find the conditions on a, b, and c so that the following linear system of equations have a solution.

−2x + y + z = a

x − 2y + z = b

x + y − 3z = c

Find the inverse of the matrix using echelon reduction method .

x + 3y - z =0

x + y + z = 1

-x + 2y - z = 1

Find the root of the equation x^2 - 3 = 0 using the bisection method.

1) correct to the four decimal places.

Find the root of the equation x^3 - x - 11 = 0 using bisection method.

up to six iterations.

Two catering firms are competing for the catering contract for the school formal

dinner. Conya Cuisine has quoted a fixed charge of K450 plus K11 per head. Fred’s

Food has quoted a fixed charge of K300 plus K12.20 per head.

i) Identify the variables and denote them with a pro-numeral.

ii) Derive the equations involving the pro-numerals.

iii) Solve the equations. What practical information is given by your solution?

iv) If 250 students are attending the dinner, which company would be cheaper?

v) How many students need to attend for the catering costs to be equal