Linear Algebra

Given the matrix

0 2 3 -4 1

0 0 2 3 4

2 2 -5 2 4

2 0 -6 9 7

Reduce to row echelon form

Find the rank of the matrix

0 2 3 -4 1

0 0 2 3 4

2 2 -5 2 4

2 0 -6 9 7

Reduce to row echelon form

Find the rank of the matrix

Linear Algebra

If a=i -j+2k, b = 4j - 2k and c = -10i - 2j +4k

Find the angle between the vectors a and c

Find |a +c |

Find the angle between the vectors a and c

Find |a +c |

Linear Algebra

2. John has a plan to distribute soft drinks in jimma town for the next year in partnership with Moha

company. He signs a contract with the general manager of Moha soft drinks to operate at a profit

margin of 40 %. Other incremental costs including selling expenses incurred while selling the drinks

in jimma town. John includes these costs at the rate of 20% in addition to the cost of soft drinks.

Further, he incurs an estimated fixed cost of Birr 60,000per year in the operation.

a. What is the linear sales-cost equation

b. What is the breakeven volume of sales in Birr per year

c. What is the retailers profit if he sold soft drinks worth Birr 400,000in a year?

d. If john has sold two crates of soft drinks at Birr 50 each, find the total cost equation

interms of quantities

company. He signs a contract with the general manager of Moha soft drinks to operate at a profit

margin of 40 %. Other incremental costs including selling expenses incurred while selling the drinks

in jimma town. John includes these costs at the rate of 20% in addition to the cost of soft drinks.

Further, he incurs an estimated fixed cost of Birr 60,000per year in the operation.

a. What is the linear sales-cost equation

b. What is the breakeven volume of sales in Birr per year

c. What is the retailers profit if he sold soft drinks worth Birr 400,000in a year?

d. If john has sold two crates of soft drinks at Birr 50 each, find the total cost equation

interms of quantities

Linear Algebra

Find the inverse of the matrix

[ 2 -5 11]

1 1 -6

4 -3 8

[ 2 -5 11]

1 1 -6

4 -3 8

Linear Algebra

A company produces two products. Each product requires a certain amount of raw material. Product A requires 3 ponds of the raw material and product B 4 pounds. For any given week, the availability of the raw material is 2,400 pounds. If x equals the number of units produced of product A and Y the number of units of product B:

Determine the equation which states that total raw material used each week equals 2,400 pounds.

Rewrite the equation in slope-intercept form and identify the slope and Y-intercept.

Interpret the values of the slope and Y-intercept.

Determine the equation which states that total raw material used each week equals 2,400 pounds.

Rewrite the equation in slope-intercept form and identify the slope and Y-intercept.

Interpret the values of the slope and Y-intercept.

Linear Algebra

Show that C^n is a complex vector space

Linear Algebra

Write the application of Linear Algebra in Computer science and Engineering.

Linear Algebra

Let (x1,x2,x3) and (y1,y2,y3) represent the coordinates with respect to the bases B1 = {(1, 0, 0),(1, 1, 0),(0, 0, 1)},B2 = {(1, 0, 0),(0, 1, 2),(0, 2, 1)}. If Q(x) = x1^2-4x1x2+2x2x3+x2^2+x3^2 , find the representation of Q in terms of (y1,y2,y3)

Linear Algebra

a) Check whether the matrices A and B are diagonalisable. Diagonalise those

matrices which are diagonalisable.

A = 1 0 0 B = 2 0 0

1 5 -3 -2 2 -1

2 8 -5 -1 0 1

b) Find inverse of the matrix B in part a) of the question by using

Cayley-Hamiltion theorem.

c) Find the inverse of the matrix A in part a) of the question by fnding its

adjoint.

matrices which are diagonalisable.

A = 1 0 0 B = 2 0 0

1 5 -3 -2 2 -1

2 8 -5 -1 0 1

b) Find inverse of the matrix B in part a) of the question by using

Cayley-Hamiltion theorem.

c) Find the inverse of the matrix A in part a) of the question by fnding its

adjoint.

Linear Algebra

Check whether the following system of equations has a solution. (6)

3x+2y+6z+4w =4

x+2y +2z +w =5

x+z+ 3w =3