Let W be the subspace of R³ spanned by the vectors P = 9 8 IN 9 0/0 0/1 0/00 Find the projection matrix P that projects vectors in IR³ onto W.

Q: Let V be the plane with equation ₁ - 3x2 - 4x3 = 0 in R³. Find the matrix A of the 1 orthogonal…

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Q: Let V be the plane with equation 2₁-522+623= 0 in R³. Find the matrix A of the orthogonal projection…

A: Given that  v=273-2  and the basis set is 510,-601 , let  u1=510 and u2=-601 part(1):…

Q: Let L be the line in R3 that consists of all scalar multiples of the vectors (1 1 1 ) . Let 2 T (~x)…

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Q: What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors a₁ =…

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Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: find all vectors v⃗  in 2 dimensions having ||v⃗ ||=41 where the j⃗ -component of v⃗  is 9j⃗ .

A: Our objective is to find all the vectors v having ||v||=41 and the j-th component 9j.

Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

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Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

A: Orthogonal projection, also known as orthogonal projection mapping or simply projection, is a…

Q: The matrix that projects onto the x-y plane is

A: We have to find the matrix that project onto  plane

Q: dy Use dsolve to solve dt ty+2y-t-2 ty-3y+t-3

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Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

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Q: Let V be the plane with equation x-2x - 4x = 0 in R. Find the matrix A of the orthogonal projection…

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Q: Find the length of the projection of 3   onto the vector -3…

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Q: The vector x is in a subspace H with a basis ß = {b₁,b₂}. Find the ß-coordinate vector of x. b₁ =…

A: The given basis is b1,b2=1-2, -53. To Find: beta coordinate vector of x=19-17 w.r.t the above basis.

Q: Let V be the subspace of P^4 spanned by B = {1,x^2,x^4}. Create a chnage of basis matrix Cd,b if D =…

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Q: Find the matrix A, relative to the standard basis {e1, e2, e3, e4}, of t

A: Given, W be the subspace of ℝ4 spanned by the vectors                                    1-11-1 and…

Q: Find a basis for the orthogonal complement of the subspace of Rª spanned by the vectors V1 = (3,…

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Q: Now try to find the projection matrix that will project vectors onto the subspace of R³ spanned by…

A: To find the projection matrix that projects vectors onto the subspace of  spanned by the vectors v₁…

Q: Construct a matrix to scale by a factor of 5 abou the plane through the origin perpendicular to the…

A: Given: To construct a matrix to scale by a factor of 5 is given as,  is the vector .

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: Let 3 -7 ,V = u -3 -3 4 and let W the subspace of R* spanned by u and v. Find a basis of w', the…

A: The given vectors are u=3-73-3, v=-12-34 and W be the subspace of R4 spanned by u and v.