Linear Algebra Answers

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.