Linear Algebra Answers

Directions: Establish the table of information and formulate the LP Model of the following:

2.) An appliance repair shop has 5 electric fans, 12 washing machines, and 18 air conditioning units to be repaired. The store employs two part-time repairmen. Repairman A can repair 3 electric fans, 3 washing machines, and 4 airconditioning units in a week, while Repairman B can repair 1 electric fan, 3 washing machines, and 6 air conditioning units in a week. repairman A is paid Php 5,000 a week and repairman B is paid Php 4,200 a week. To minimize cost how many weeks should each of the two repairmen be employed?

Proof whether the following operations are inner product operations:

⟨x, y⟩ = 2x₁y₁ − x₁y₂ − x₂y₁ + 2x₂y₂, x=(x₁, x₂), y=(y₁, y₂)

Proof whether the following operations are inner product operations:

⟨x, y⟩ = 2x₁y₁ − x₁y₂ − x₂y₁ + 2x₂y₂, x=(x₁, x₂), y=(y₁, y₂)

Consider the basis for , where , , and , and let t:R^3 -> R^2 be the linear transformation for which T(v1)=(-1,0), T(v2)=(-1,1), T(v3)=(0,1). Find a formula for T(x1, x2, x3), and use that formula to find T(7,13,7)

given P2 as the vector space of all real polynomials of degree less than or equal to two. Let W be a subspace of P2 specified by W= {a0 + a1x + a2x^2 where a0 -a1 =0}. Determine whether W is a subspace of P2.

determine whether the set s={(a,b,c) ; ab=1} is a subspace of R3

Find the number of ordered pairs (x;y) of positive integers satisfying 1/x + 1/y = 1/(2021 ^ 17)

If x ≠ y then pairs (x;y) and (y;x) are considered to be different.

Let V = R3 and let W = {(x, y, z)  R3| z = x + y}. Prove that W is a subspace of V.

Solve the following pair of linear equation by matrix method 2p +q =5

5p +3=11

Prove that a scalar and vector can be added.