Linear Algebra Answers

Let S={(1,4),(0,3)} be a subset of R^2(R).prove that (2,3) belongs to L(S)

Find a basis for the null space, row space and column space of matrix

if 2,-1,-3 are the eigen values of the matrix A then find the eigen values of the matrix A Inverse

Find the sum and product of the matrix of the given eigen values of the matrix
A=2 1 2
1 3 1
2 2 -6

Solve the system of following equation by guass elimination method
3x1+2x2+6x3=2
6x1-7x2-11x3=8
-5x1+9x2+3x3=10

Choose h and k such that the system below has (a) no solution, (b) a unique solution, and (c)
many solutions.

x1 + 3x2 = 2

3x1+ hx2 = k.

Find the general solutions of the systems whose augmented matrices is given?

[ 3 -4 2 0 ]
[ -9 12 -6 0 ]
[ -6 8 -4 0 ]

A Leading mobile phone manufacturer is about to introduce a new series, initially they are launching 4 models of the same series. The accompanying table summarizes price and variable costs data, combined fixed costs equal $540,000.



Models



Infinity A Pro Max

Infinity A Pro

Infinity A

Infinity A Lite

Selling Price (in dollars)

500

400

340

220

Material Cost /unit (in dollars)

220

190

150

90

Labor Cost/unit (in dollars)

90

65

65

50

Table 1

a) Develop a joint total revenue function for sales of the four different models.

b) Develop an annual total cost function for manufacturing the four models.

c) Develop the profit function for sales of the four models.

d) Calculate the annual profit if the firm sells 9000, 12000, 45000 and 22000 units, respectively, of the four models?