Give an orthogonal basis for R3 that contains the vector [1,2,2]T,

Expert Solution

Colby Messinger answered 2 years ago

Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x,...

Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x, y, z) = (y − z, x − z, x − y), B' = {(5, 0, −1), (−3, 2, −1), (4, −6, 5)}

Vector v=(9,0,2) is vector from R3 space. Consider standard inner product in R3. Let W be...

Vector v=(9,0,2) is vector from R3 space. Consider standard inner product in R3. Let W be a subspace in R3 span by u = (9,2,0) and w=(9/2,0,2). a) Does V belong to W? show explanation b) find orthonormal basis in W. Show work c) find projection of v onto W( he best approximation of v with elements of w) d) find the distance between projection and vector v

A) Create two vectors in R3 ( 3D vectors) such that they are orthogonal. b) Using...

A) Create two vectors in R3 ( 3D vectors) such that they are orthogonal. b) Using the two vectors from a) above, determine the cross product of the two vectors c)Is it possible to write the vector [0,0,1] using scalar multiples of these vectors?

V is a subspace of inner-product space R3, generated by vector u =[1 1 2]T and...

V is a subspace of inner-product space R3, generated by vector u =[1 1 2]T and v =[ 2 2 3]T. T is transpose (1) Find its orthogonal complement space V┴ ; (2) Find the dimension of space W = V+ V┴; (3) Find the angle q between u and v; also the angle b between u and normalized x with respect to its 2-norm. (4) Considering v’ = av, a is a scaler, show the angle q’ between u...

Let u and v be orthogonal vectors in R3 and let w = 3u + 6v....

Let u and v be orthogonal vectors in R3 and let w = 3u + 6v. Suppose that ||u|| = 5 and ||v|| = 4. Find the cosine of the angle between w and v.

Find a matrix representation of transformation T(x)= 2x1w1+x2w2-3x3w3 from R3 to a vector space W, where...

Find a matrix representation of transformation T(x)= 2x1w1+x2w2-3x3w3 from R3 to a vector space W, where w1,w2, and w3 ∈ W. Clearly state how this matrix is representing the transformation.

Choose your favorite unique vector b in R3 with no 0 entries. What is your vector...

Choose your favorite unique vector b in R3 with no 0 entries. What is your vector b? Based on the “Equivalent Conditions for a Non-Singular Matrix” on page 123 in our text, why must Ax = b have a unique solution in this situation? Solve the equation Ax = b the following three ways (you should get the same answer each way!) Recall – calculator OK, in fact suggested. (24 points – 8 points each) Solve the equation Ax =...

Find the vector and parametric equations for the plane. The plane that contains the lines r1(t)...

Find the vector and parametric equations for the plane. The plane that contains the lines r1(t) = <6, 8, 8,> + t<-2, 9, 6> and r2 = <6, 8, 8> + t<5, 1, 7>.

Let T : R2 → R3 be a linear transformation such that T( e⃗1 ) =...

Let T : R2 → R3 be a linear transformation such that T( e⃗1 ) = (2,3,-5) and T( e⃗2 ) = (-1,0,1). Determine the standard matrix of T. Calculate T( ⃗u ), the image of ⃗u=(4,2) under T. Suppose T(v⃗)=(3,2,2) for a certain v⃗ in R2 .Calculate the image of ⃗w=2⃗u−v⃗ . 4. Find a vector v⃗ inR2 that is mapped to ⃗0 in R3.

Prove the following T is linear in the following definitions (a) T : R3 →R2 is...

Prove the following T is linear in the following definitions (a) T : R3 →R2 is defined by T(x,y,z) = (x−y,2z) (b) T : R2 →R3 is defined by T(x,y) = (x−y,0,2x+y) (c) T : P2(R) → P3(R) is defined by T(f(x)) = xf(x)+f(x)

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