3) Let a real. S = {x, Bry ) T = { α₁ B₁ α + B₁ B + √y be subsets of show that L(S) = L (T) vector space V.

Q: The set of vectors in R? with y = -3x is a real vector space

A:

Q: (a) Give examples of three distinct vectors v1, v2, v3 in the vector space R3 such that v2 E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: Show that λis a root of char(x) if and only if there exosts a non-zero vector v in V with L(v)=λv

A: Assume that λ is a root of charL(x) then | λIdv–L | = 0. It is known that, the system of Bx = 0 has…

Q: Show that W is a vector space.

A:

Q: w that the space V = {(x1, x2, x3) ∈F3

A: To prove that the space V=(x1, x2, x3)∈F3|x1+2x2+2x3=0 forms a vector space.

Q: Let V be a K-vector space and U1, U2, U3 three sub-vector spaces of V. Show that: dim(U1) + dim(U2)…

A: first of all we must know about the dimension of the vector space.what is the dimension of the…

Q: Show that the set of polynomials of degree 3 form a vector space. P(x) = ax³ + bx² + cx+d, a, b, c,…

A: We can show that the set of all polynomials of degree 3, where P(x) = x^3 + bx^2 + cx + d (a, b, c,…

Q: Suppose a, b, and c are positive real numbers satisfying a2 = b2 + c2. r(t) =…

A:

Q: Suppose that u, u and w are vectors in a real inner product space such that (u, w) = 16, (v, w) = 5,…

A: Instead of u¯,v¯,w¯ , we are writing u,v,w. (for sake of convenience). Given: (i) <u,w>=16(ii)…