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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
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 |
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
Find the inverse of the matrix
[ 2 -5 11]
1 1 -6
4 -3 8
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.
Show that C^n is a complex vector space
Write the application of Linear Algebra in Computer science and Engineering.
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)
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.

 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


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