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Homework Answers
The Let s1(t) and s2(t) be defined below:
The Let s1(t) and s2(t) be defined below: (a) Find an orthonormal basis for S= span{s1(t) and s2(t)}.(b) If y1(t) = 1, find and sketch ý1(t), the projection of y1(t) onto S.
3 y+ z 0 2. Let W be a plane characterized by the equation W. D...
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the orthogonal projection of R onto W 2) Find the distance between a vector (2, 2, 15) and the plane W. (5 (3
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the...
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0...
How can I get the (a) 3*2 matrix A?
x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
+1 (a) (3 points) Find the projection of -300 onto the span of 0 (b) (3...
+1 (a) (3 points) Find the projection of -300 onto the span of 0 (b) (3 points) Find the projection of onto the span of (c) (4 points) Observe that H = 1 V2 has orthonormal columns. Note that 1 = 2 +1 +1 +1 +1 +1 +1 -1 H H H2 can be written as a block matrix as H2 +1 +1 -1 -1 V2 H -H1 +1 H2 H2 and an 8 x 8 matrix H3 can be...
0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are...
0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5 0.5 0.5 -1 -2 (a) Solve the least squares problem Ax = b where b - -2 0 (b) Find the projection matrix P that projects vectors in R4 onto R(A) P = (c) Compute Ax and Pb Pb =
0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5...
(1 point) Are the following statements true or false? ? 1. The best approximation to y...
(1 point) Are the following statements true or false? ? 1. The best approximation to y by elements of a subspace W is given by the vector y - projw(y). ? 2. If W is a subspace of R" and if V is in both W and Wt, then v must be the zero vector. ? 3. If y = Z1 + Z2 , where z is in a subspace W and Z2 is in W+, then Z, must be...
3 0 6 (a) Let x1 = 2 X2= and write W = span{X1, X2} 21...
3 0 6 (a) Let x1 = 2 X2= and write W = span{X1, X2} 21 Find X1 X2 and enter your answer in the box below. X1 X2 = Number We then apply Gram-Schmidt to find an orthonormal basis for W. V1 = X1 v2 = x2 - projv112 Find V2 and enter your answer in the box below. We then normalise the basis {V1, V2} to form an orthonormal basis {01, 12} (0) in Maple syntax, should be...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to uị and u2 span(uj, u2), then z must be in and if W = Wt. ? 2. For each y and each subspace W, the vector y – projw(y) is orthogonal to W. ? 3. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. ? 4. The orthogonal projection p of y onto a subspace...
1. Let A 1 2 3 1 2 1 (a) Compute l|Alli Allo AF b) Write out the first three steps of the power m...
1. Let A 1 2 3 1 2 1 (a) Compute l|Alli Allo AF b) Write out the first three steps of the power method for A with the initial vector [1,o,oT. (c) Find a QR decomposition for A. (d) Find (e) Compute the condition number Ro(A) corresponding to oo-norm. an orthogonal projection whose range is spanned by the first two columns of A.
1. Let A 1 2 3 1 2 1 (a) Compute l|Alli Allo AF b) Write...
20 3. Let 1 = 2 and = 5. Let W = Span{11, 13). (a) Give...
20 3. Let 1 = 2 and = 5. Let W = Span{11, 13). (a) Give a geometric description of W. (b) Use the Gram-Schmidt process to find an orthogonal basis for W. (c) Let = 2 Find the closest point to į in W. (a) Use your orthogonal basis in part (b) to find an orthonormal basis for W.
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the orthogonal projection of R onto W 2) Find the distance between a vector (2, 2, 15) and the plane W. (5 (3
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the...
How can I get the (a) 3*2 matrix A?
x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
+1 (a) (3 points) Find the projection of -300 onto the span of 0 (b) (3 points) Find the projection of onto the span of (c) (4 points) Observe that H = 1 V2 has orthonormal columns. Note that 1 = 2 +1 +1 +1 +1 +1 +1 -1 H H H2 can be written as a block matrix as H2 +1 +1 -1 -1 V2 H -H1 +1 H2 H2 and an 8 x 8 matrix H3 can be...
0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5 0.5 0.5 -1 -2 (a) Solve the least squares problem Ax = b where b - -2 0 (b) Find the projection matrix P that projects vectors in R4 onto R(A) P = (c) Compute Ax and Pb Pb =
0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5...
(1 point) Are the following statements true or false? ? 1. The best approximation to y by elements of a subspace W is given by the vector y - projw(y). ? 2. If W is a subspace of R" and if V is in both W and Wt, then v must be the zero vector. ? 3. If y = Z1 + Z2 , where z is in a subspace W and Z2 is in W+, then Z, must be...
3 0 6 (a) Let x1 = 2 X2= and write W = span{X1, X2} 21 Find X1 X2 and enter your answer in the box below. X1 X2 = Number We then apply Gram-Schmidt to find an orthonormal basis for W. V1 = X1 v2 = x2 - projv112 Find V2 and enter your answer in the box below. We then normalise the basis {V1, V2} to form an orthonormal basis {01, 12} (0) in Maple syntax, should be...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to uị and u2 span(uj, u2), then z must be in and if W = Wt. ? 2. For each y and each subspace W, the vector y – projw(y) is orthogonal to W. ? 3. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. ? 4. The orthogonal projection p of y onto a subspace...
1. Let A 1 2 3 1 2 1 (a) Compute l|Alli Allo AF b) Write out the first three steps of the power method for A with the initial vector [1,o,oT. (c) Find a QR decomposition for A. (d) Find (e) Compute the condition number Ro(A) corresponding to oo-norm. an orthogonal projection whose range is spanned by the first two columns of A.
1. Let A 1 2 3 1 2 1 (a) Compute l|Alli Allo AF b) Write...
20 3. Let 1 = 2 and = 5. Let W = Span{11, 13). (a) Give a geometric description of W. (b) Use the Gram-Schmidt process to find an orthogonal basis for W. (c) Let = 2 Find the closest point to į in W. (a) Use your orthogonal basis in part (b) to find an orthonormal basis for W.
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