Linear Algebra Answers

Write v = (2, -5 , 3) as a linear combination of

u1=(1,−3 ,2)

u2=(2,−4 ,−1)

u3=(1,−3 , 7)

Write the equations in matrix form :

x-y=-5

3x+2y=-5

A department store has overhead costs of $250; 000 and a linear total cost function. The controller has set the

store's margin policy using the example of a $140 markup on an item retailing for $500. The controller has also

estimated that other variable costs on the same retail item selling for $500 are $15.

i. Find the revenue, cost, and prot functions using s for sale volume.

ii. Find the break-even dollar volume of sales.

iii. Draw the break-even chart.

iv. What will the net prot be if sales are $3; 000; 000 ?

Consider the linear eigenproblem, 𝐴𝑥=𝜆𝑥, for the matrix

D=[1 1 2

2 1 1

1 1 3 ]

Solve for the largest eigenvalue by the direct method using the secant method. Let 𝜆^((0))=5 and 𝜆^((1))=4 Solve for the eigenvalues by the QR method

(a) Let A=   be a matrix representing the linear transformation T
 i. Find the image of V = [−1, 2, 5] under T(2marks)
 ii. Determine the kernel or nullspaceof T(5marks)
Find the range and rank of T (3marks) 


(b) let T: R3 ... > R3 be defined by T (x, y, z) = (x + y, x − y, y + z)
Find the matrix representing T with respect to standard basis(3marks)
Find the kernel and nullity of T (4marks)
find Range and Rank of T(3marks) 


c) Let A=      be a matrix representing A respect to the standard under basis R3 
Find the image of V = [−2, 1, 2] under T (4marks)
Determine the kernel of T (3marks)
Find the rank of T (3marks) 

"W = {(x, y, z) \u2208R3|3x \u22122y + 4z = 0}."

Let W be the set of vectors in R³ of the form(a,b,½a-2b)

show that W is subspace of R³

Let W={(X,Y,Z)|x+y+z=0}

A, give a basis for W

B, what is the dimension of W

Show that the set of vectors {(1,1,5),(1,1,3)(1,1,3)}

it is linear independent or not

Micros Unlimited corporation (a local distributor of micro computers) sells one of its 586-based system on a volume

discount as follows: 1 to 5 units at a price of $4495 per unit, units 6 through 10 at a price of $ 4095 per unit, and

any unit in excess of 10 at a price of $3775 per unit.

i. Determine the cost function and draw its graph.

ii. What are the total and average cost s of 4 units ?

iii. What are the total and average cost s of 15 units?

iv. How many units were purchased if the total charge was $58,050 ?

v. How many units were purchased if the average charge was $4035?