3. If Pa(b) is the projection of vector b along vector a, show algebraically (not geometrically) and that Pd (b) b-Pa(b) is perpendicular to a. Derive general expressions for Pa(b)l P (b)l 3. If...
Problem 1. Given the vector space Pa, the basis B =< 1,7,22,,24 > of Pd, let U = span[1, 2], V = span[22, 1) and W = span[r2,, ). Which of the following statements is true? 1. UmV = 0 2. UUV is a vector subspace of P. 3. U W = 0 and for any vector subspace P of PA, U, W CP 4. UUW =P 5. All except statement 3 is false. P =P.
7. A point P moves along the spiral rae20 with constant speed u. Show that the components of its velocity along and perpendicular to the radius vector are constant. Find in terms of u and r the magnitude of the resultant acceleration of P. Find the angle between this acceleration and the velocity of P
7. A point P moves along the spiral rae20 with constant speed u. Show that the components of its velocity along and perpendicular to the...
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. b) Find the least squares approximation, £, to the solution vector x of Ai- c) The least squares error is defined to be the length of the vector b - AX. Find this vector and its length. d) What is the relationship between A, , and p?
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto...
show all work please, thanks
Find the projection of vector v onto line L.
v = <5,-1,2>, L: x=3,
y + 4 22 3 # 1 , 2: Find the projection of vector 1. =(5,-1,2), l: x = onto line f. y+4 3, -1 Z-2 3
y + 4 22 3
# 1 , 2: Find the projection of vector 1. =(5,-1,2), l: x = onto line f. y+4 3, -1 Z-2 3
(1 point) What is the matrix P-(P) for the projection of a vector b є R3 onto the subspace spanned by the vector a- ? 5 9 Pl 3 1 2 P21 23 - P32 31 What is the projection p of the vector b0onto this subspace? 9 Pl Check your answer for p against the formula for p on page 208 in Strang.
(1 point) What is the matrix P-(P) for the projection of a vector b є R3...
Projection vector, p, of w on V V = (6,6) p = (4.4) W = (6,2) 1 2 3 4 5 6 Visualising vector projection Exercise 2 The projection of w= is given by the projection formula below: Plot all three vectors using plot and make the projection vector pa dashed line. Write a script from scratch to produce the figure below (click to enlarge). Make sure the axes are equal. Show/hide hint Optional extra challenge Upload your M-file that...
(7) Let V be a finite-dimensional vector space over F, and PE C(V) In this question, we will show that P is an orthogonal projection if and only if P2P and PP It may be helpful to recal that P is the orthogonal projection onto a subspace U if and only if (1) P is a projection, and (2) ran(P)-U and null(P)U (a) Prove that if P is an orthogonal projection, then P2P and P is self-adjoint Hint: To show...
show work please
Written Homework 10, Due May 2 Name 3. (11 point) (a) (5 points) Find the projection of the vector (3,4) onto the vector (0,6). Sketch a picture of these vectors and its projection vector. (b) (6 points) Find a vector parallel to the vector (3,4) whose projection onto the vector (06) is equal to (0.2). Page 3
Written Homework 10, Due May 2 Name 3. (11 point) (a) (5 points) Find the projection of the vector (3,4)...
SHOW ALL WORK!!!
2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
Full answers and working out please.
B -B (A+B) (B+A) (A-B) B FIGURE 1.3 FIGURE 1.4 (1) Addition of two vectors. Place the tail of B at the head of A; the sum, A+B, is the vector from the tail of A to the head of B (Fig. 1.3). (This rule generalizes the obvious procedure for combining two displacements. Addition is commutative: A+B=B+A; 3 miles east followed by 4 miles north gets you to the same place as 4 miles...