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Linear Algebra
Show necessary step for the following questions
("For the given matrix"
A=the first row [1 -1] second row [3 2]
B=the first row [3 -2] second row [0 1]
1) show that (A^t)^t=A
2) show that (A+B)^t=A^t+B^t
3) show that (4A)^t=4(A^t)
4) show that (AB)^t=A^tB^t)
("For the given matrix"
A=the first row [1 -1] second row [3 2]
B=the first row [3 -2] second row [0 1]
1) show that (A^t)^t=A
2) show that (A+B)^t=A^t+B^t
3) show that (4A)^t=4(A^t)
4) show that (AB)^t=A^tB^t)
Linear Algebra
(1) Let;
- A=the first row [-1 -1] second row [3 3]. Find all 2×2 materices, B such that AB=0
(2) Distinguish whether the given matrix is symmetric or not
- A=the first row [2 1 3] second row [1 5 -3] third row [3 -3 7]
- B=the first row[1 1 3] second row[1 2 2] third row[3 2 3]
Linear Algebra
Suppose A and B are 3 × 3 matrices. Prove that
(i) (A + B)^T = B^T + A^T
(ii) det (AB)^T = det (A). det (B)
(i) (A + B)^T = B^T + A^T
(ii) det (AB)^T = det (A). det (B)
Linear Algebra
Suppose A and B are 3 × 3 matrices. Show that If B is obtained from A by adding 2 times the first row of A to the last row of A, then
det (A) = det (B)
Linear Algebra
Represent the electricity bill using a linear equation in 2 variable with respect to fixed charge and unit consumption in the month of April 2020, May 2020 and December 2019.Find the reason behind the variation of electricity bill explaining the use of different electric appliances
Linear Algebra
A company manufactures two types of wedding dresses, mermaid and ballroom style for sale. The
mermaid makes a profit of N$1000 and ballroom makes a profit of N$850. The manufacture of each
of the dresses involves 3 parts, designing, cutting and sewing. The mermaid requires 12hours of
designing, 9 hours of cutting and 30 hours of sewing. The ballroom requires 24hours of designing, 5
hours of cutting and 30 hours of sewing. Due to the number of employees available at the company
there is at most 480 hour available for designing, 180 hours for cutting and 720 hours for sewing.
Assume that the company can sell all the wedding dresses it manufactures, find the maximum number
of each type of wedding dress the company should manufacture to maximize profit.
mermaid makes a profit of N$1000 and ballroom makes a profit of N$850. The manufacture of each
of the dresses involves 3 parts, designing, cutting and sewing. The mermaid requires 12hours of
designing, 9 hours of cutting and 30 hours of sewing. The ballroom requires 24hours of designing, 5
hours of cutting and 30 hours of sewing. Due to the number of employees available at the company
there is at most 480 hour available for designing, 180 hours for cutting and 720 hours for sewing.
Assume that the company can sell all the wedding dresses it manufactures, find the maximum number
of each type of wedding dress the company should manufacture to maximize profit.
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
