Question

Let A = [1 5 ; 3 1 ; 2 -4] and b = [1 ;...

Let A = [1 5 ; 3 1 ; 2 -4] and b = [1 ; 0 ; 3] (where semicolons represent a new row)

Is equation Ax=b consistent?

Let b(hat) be the orthogonal projection of b onto Col(A). Find b(hat).

Let x(hat) the least square solution of Ax=b. Use the formula x(hat) = (A^(T)A)^(−1) A^(T)b to compute x(hat). (A^(T) is A transpose)

Verify that x(hat) is the solution of Ax=b(hat).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b onto a....
1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b onto a. proj a b= 2) Find the area of a triangle PQR, where P=(−2,−4,0), Q=(1,2,−1), and R=(−3,−6,5) 3) Complete the parametric equations of the line through the points (7,6,-1) and (-4,4,8) x(t)=7−11 y(t)= z(t)=
Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))...
Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2)) 14. (3 points) Let B1 be the basis for M you found by row reducing M and let B2 be the basis for M you found by row reducing M Transpose . Find the change of coordinate matrix from B2 to B1.
T: R^3 ----> R^5 such that T(x), then... a. A^-1 is 3x 5 matrix b. the...
T: R^3 ----> R^5 such that T(x), then... a. A^-1 is 3x 5 matrix b. the mapping cannot be onto c. the set of solutions to Ax=0 is infinite d. A has at least 2 free variables e. none of the above
Consider W = Span{p1(t),p2(t)} where p1(t) = 1−t^2 and p2(t) = 3+2t are the polynomials defined...
Consider W = Span{p1(t),p2(t)} where p1(t) = 1−t^2 and p2(t) = 3+2t are the polynomials defined on the interval [−1,1]. Find the orthogonal projection of q(t) = t^2−t−1 onto W.
Let V be the vector space of 2 × 2 matrices over R, let <A, B>=...
Let V be the vector space of 2 × 2 matrices over R, let <A, B>= tr(ABT ) be an inner product on V , and let U ⊆ V be the subspace of symmetric 2 × 2 matrices. Compute the orthogonal projection of the matrix A = (1 2 3 4) on U, and compute the minimal distance between A and an element of U. Hint: Use the basis 1 0 0 0   0 0 0 1   0 1...
Consider the following. u = −6, −4, −7 ,    v = 3, 5, 2 (a) Find the...
Consider the following. u = −6, −4, −7 ,    v = 3, 5, 2 (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v.
U= [2,-5,-1] V=[3,2,-3] Find the orthogonal projection of u onto v. Then write u as the...
U= [2,-5,-1] V=[3,2,-3] Find the orthogonal projection of u onto v. Then write u as the sum of two orthogonal vectors, one in span{U} and one orthogonal to U
1. Find the orthogonal projection of the matrix [[3,2][4,5]] onto the space of diagonal 2x2 matrices...
1. Find the orthogonal projection of the matrix [[3,2][4,5]] onto the space of diagonal 2x2 matrices of the form lambda?I.   [[4.5,0][0,4.5]]  [[5.5,0][0,5.5]]  [[4,0][0,4]]  [[3.5,0][0,3.5]]  [[5,0][0,5]]  [[1.5,0][0,1.5]] 2. Find the orthogonal projection of the matrix [[2,1][2,6]] onto the space of symmetric 2x2 matrices of trace 0.   [[-1,3][3,1]]  [[1.5,1][1,-1.5]]  [[0,4][4,0]]  [[3,3.5][3.5,-3]]  [[0,1.5][1.5,0]]  [[-2,1.5][1.5,2]]  [[0.5,4.5][4.5,-0.5]]  [[-1,6][6,1]]  [[0,3.5][3.5,0]]  [[-1.5,3.5][3.5,1.5]] 3. Find the orthogonal projection of the matrix [[1,5][1,2]] onto the space of anti-symmetric 2x2 matrices.   [[0,-1] [1,0]]  [[0,2] [-2,0]]  [[0,-1.5] [1.5,0]]  [[0,2.5] [-2.5,0]]  [[0,0] [0,0]]  [[0,-0.5] [0.5,0]]  [[0,1] [-1,0]] [[0,1.5] [-1.5,0]]  [[0,-2.5] [2.5,0]]  [[0,0.5] [-0.5,0]] 4. Let p be the orthogonal projection of u=[40,-9,91]T onto the...
1) Consider two vectors A=[20, 4, -6] and B=[8, -2, 6]. a) compute their dot product...
1) Consider two vectors A=[20, 4, -6] and B=[8, -2, 6]. a) compute their dot product A.B b) Compute the angle between the two vectors.    c)Find length and sign of component of A over B (mean Comp A over B)and draw its diagram.    d) Compute Vector projection of B over A (means Proj B over A) and draw corresponding diagram. e) Compute Orthogonal projection of A onto B.
Let A be a given (3 × 3) matrix, and consider the equation Ax = c,...
Let A be a given (3 × 3) matrix, and consider the equation Ax = c, with c = [1 0 − 1 ]T . Suppose that the two vectors x1 =[ 1 2 3]T and x2 =[ 3 2 1] T are solutions to the above equation. (a) Find a vector v in N (A). (b) Using the result in part (a), find another solution to the equation Ax = c. (c) With the given information, what are the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT