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(12 points) Let vi = 1 and let W be the subspace of R* spanned by...
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A- (3 points) Let W be the subspace of R spanned by the vectors 1and 5 F...
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1),...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
(1 point) Let W be the subspace of R spanned by the vectors 27 1 and...
(1 point) Let W be the subspace of R spanned by the vectors 27 1 and -7 Find the matrix A of the orthogonal projection onto W. A =
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3...
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3), and let W be the subspace spanned by B. Note that B is an orthogonal set. 17 a. 1 point] Find the coordinates of uwith respect to B, without inverting any matrices or L-2 solving any systems of linear equations. 35 16 25 b. 1 point Find the orthogonal projection of to W, without inverting any matrices or solving any systems of...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1...
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1 and 4 Find the projection matrix P that projects vectors in R3 onto W
1) Determine if w is in the subspace spanned by v1, v2, v3 2) Are the...
1) Determine if w is in the subspace spanned by v1, v2,
v3
2) Are the vectors v1, v2, v3 linearly dependent or
independent? justify your answer
Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
Find the orthogonal projection of v = |8,-5,-5| onto the subspace W of R^3 spanned by...
Find the orthogonal projection of v = |8,-5,-5| onto the
subspace W of R^3 spanned by |7,-6,1| and |0,-5,-30|.
(1 point) Find the orthogonal projection of -5 onto the subspace W of R3 spanned by 7 an 30 projw (V)
Will rate once all is completed. 1) 2) 3) 4) (12 points) Find a basis of...
Will rate once all is completed.
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4)
(12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
Let W be the subspace of R3 spanned by the vectors ⎡⎣⎢113⎤⎦⎥ and ⎡⎣⎢4615⎤⎦⎥. Find the projection matrix P that project...
Let W be the subspace of R3 spanned by the vectors ⎡⎣⎢113⎤⎦⎥ and ⎡⎣⎢4615⎤⎦⎥. Find the projection matrix P that projects vectors in R3 onto W.
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
(1 point) Let W be the subspace of R spanned by the vectors 27 1 and -7 Find the matrix A of the orthogonal projection onto W. A =
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3), and let W be the subspace spanned by B. Note that B is an orthogonal set. 17 a. 1 point] Find the coordinates of uwith respect to B, without inverting any matrices or L-2 solving any systems of linear equations. 35 16 25 b. 1 point Find the orthogonal projection of to W, without inverting any matrices or solving any systems of...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1 and 4 Find the projection matrix P that projects vectors in R3 onto W
1) Determine if w is in the subspace spanned by v1, v2,
v3
2) Are the vectors v1, v2, v3 linearly dependent or
independent? justify your answer
Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
Find the orthogonal projection of v = |8,-5,-5| onto the
subspace W of R^3 spanned by |7,-6,1| and |0,-5,-30|.
(1 point) Find the orthogonal projection of -5 onto the subspace W of R3 spanned by 7 an 30 projw (V)
Will rate once all is completed.
1)
2)
3)
4)
(12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
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