Problem #10: Let W be the plane with the equation 7x-y + 5z = 0. Find the standard matrix P for the orthogonal projectiononto W. Use the following formulaP = = A(ATA) ¹AT,where the matrix A is constructed using any basis for Was its column vectors.Enter the first row of the matrix P (in order) into the answer box below, separated with commas. i.e., enter thevalues p11, P12, P13.Problem #10:Enter your answer symbolically,as in these examples

Answered: Image /qna-images/answer/e87bdfcf-2204-487c-bf84-7db1f404cf2d.jpg

Answered: Problem #10: Let W be the plane with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let the basis B = {b1, b2} and basis C = {c1, c2} where vectors b1 = (7 -2). b2 = 2 -1 , c1 = 4 1 c2= 5 2 Find the change of coordinates matrix from B to C. (b) Find the change of coordinates matrix from C to B.
Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R = (0, 1, -1) 8 0-0-0- y = + S 8 Z -4 -6 + t
8. A theme that will later unfold concerns the use of coordinate systems. We can identify the point (x, y) with the tip of the vector drawn emanating from the origin. We can then think of the usual Cartesian coordinate system in terms of linear combinations of the vectors ej = e2 = V2 V1 (2, –3) 42,–3} Figure 2.1.8. The usual Cartesian coordinate system, defined by the vectors ej and e2, is shown on the left along with the representation of the point (2, -3). The right shows a nonstandard coordinate system defined by vectors v1 and v2. The point (2, -3) is identified with the vector — 2е1 — Зе2. If we have vectors v1 = ,v2 = we may define a new coordinate system, such that a point {x, y} will correspond to the vector xv1 + yv2. For instance, the point {2, –3} is shown on the right side of Figure 2.1.8 Write the point {2, –3} in standard coordinates; that is, find r and y such that а. (», у) 3 {2, —3}. b. Write the point (2, –3) in the new coordinate system; that is, find a and b such…
Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is translation by (1, 4, 3). To blow up the picture around the center point (1, 4, 3), would you use vST or vT S?
An electronics company has two production facilities, denoted A and B. During an average week, facility A produces 2000 computer monitors and 10,000 flat panel televisions, and facility B produces 4000 computer monitors and 18,000 flat panel televisions. (a) Give vectors a and b that give the weekly production amounts at A and B, respectively. a = 2000 10000 (b) Compute 6b. eBook 24000 108000 b = 4000 Describe what the entries tell us. 18000 The company produces 24000 5 3 computer monitors flat panel televisions computer monitors and 108000 (c) Determine the combined output from A and B over a 5-week period. computer monitors 30000 flat panel televisions 140000 flat panel televisions at facility B in 6 (d) Determine the number of weeks of production from A and B required to produce 32,000 monitors and 152,000 televisions. facility A X weeks facility B X weeks weeks.
Please use matrix to solve.
3. What is the component and projection of the vector A x B into the vector N = 0.87 + 0.6k , if the vector Å = (10, 16, 3) and B = (5,-2, 2).
Moving to the next question prevents changes to this answer. Question 1 Given the vectors A = 4a -10a-5a P B=a+2a-7a₂ Evaluate the following (-3)|A| 3a O-0.8477a - 19.6954a+28.9338a_ p O 2.9820a +0.9431a +37.5569a P 7 P O 2.1143a -22.5451a + 13.4991a o p P O 0.2345a +12.5643a-21.4043a A Moving to the next question prevents changes to this answer.
18. Find the orthogonal projection of the vector a = (-9, -8, 7) in the direction of the vector b = (-3,-5,-2).
Consider the following vectors: u = (1, −2, −1), v = (-2, 1, 8) Without using the cross product, find a vector n which is orthogonal to both u and U. You need to use a notion from chapter 5 to set up a system of linear equations, then use RREF to solve the system. Explain why this method works.
Suppose we have three points in 3D space: P = (1,0, 1), Q = (2, 1, –1), and R= (0, –1,3) (a) Find the two vectors: ở:= PQ and w := Pहे (b) Find the dot product of the two vectors, ở- w (c) Find the product of the magnitudes, ||ö|| - |||| (d) ' rind the angle 0 between v and w (e) Find the cross product i x ở

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