What is the subspace of P2?

What is the subspace of P2?

Since every polynomial of degree up to 2 is also a polynomial of degree up to 3, P2 is a subset of P3. And we already know that P2 is a vector space, so it is a subspace of P3.

What is P2 in linear algebra?

Linear algebra -Midterm 2. 1. Let P2 be the space of polynomials of degree at most 2, and define the linear transformation T : P2 → R2 T(p(x)) = [p(0) p(1) ] For example T(x2 + 1) = [1 2 ] .

What is the dimension of P2?

The dimension of P2 is three.

Is a subspace of R2?

A subspace is called a proper subspace if it’s not the entire space, so R2 is the only subspace of R2 which is not a proper subspace.

Is R2 subspace of R3?

Originally Answered: In linear algebra, is R2 a subspace of R3? No. is isomorphic to a subspace of , but it is not actually contained in . It’s not often that you need to worry about that distinction, but it is there.

What is the subspace test?

In other words, to test if a set is a subspace of a Vector Space, you only need to check if it closed under addition and scalar multiplication. Easy! ex. Test whether or not the plane 2x + 4y + 3z = 0 is a subspace of R3.

Which of the following is basis of p2?

Solution: First we recall that the standard basis of P2(R) is β = {1, x, x2} and that the standard basis of R2 is γ = {(1,0),(0,1)}. Now we look at the image of each element of the basis β under T. T(1) = (1,0), T(x) = (0,1), and T(x2) = (0,2).

What are all the subspaces of R2?

Theorem. (a) The subspaces of R2 are 10l, lines through origin, R2. (b) The subspaces of R3 are 10l, lines through origin, planes through origin, R3.

How many subspaces does R 2 have?

It goes: “Show that the Only Subspaces of R2 are the zero subspace, R2 itself, and the lines through the origin.” I’m thinking the easiest way to do this is to show that if W is a subspace of R2 containing 2 different lines through the origin then W is all of R2.

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