(4) Find a least-square solution of Ax = b by finding orthogonal projection of b to ColA, where)()154A =31andb =-2-24-3(Note that the column vectors of A are orthogonal.)

Ax=bwhere, A=1531-24 and b=4-2-3orthogonal projectiona1=13-2 and a2=514 are column of A because…

Answered: Find a least-square solution of Ax = b…

Find a least-square solution of Ax = b by finding orthogonal projection of b to ColA, where 1 4 A= 1 and b = -2 -2 4 -3 (Note that the column vectors of A are orthogonal.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Find a vector orthogonal to both 7 -10 and w -10 -10 -4 7

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is v = 2i -2j +k u = -4i-4j +5k two vector a & b said to be…

Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

Q: 12 2 Determine if the pair of vectors v₁ = 3 V₂ = =-3 are orthogonal. -5 3

A: We have to find whether the given two vectors are orthogonal or not?

Q: how that vectors[ A-2i+ 3j - 2k,B=I +2j+ 4k ] are perpendicular to each o

Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: 5.) Let V₁ = - -2 V₂: Is b a linear combination X₁V₁ + x₂ V₂ = b. 5 b=4 of v₁ and v2; that is, does…

A: Here we have to check whether the given vector b→=745 is linear combination of vectors v1→=1-2-5 and…

Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

Q: Approximate proju and projw. -8 -7 -6 -5 -4 -3 -2 -1 proj u 5.491 projw 4.801 = vector u vector w -5…

A: Given thatWe have to approximate Projwu and Projuw.We know that

Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

Q: Multiply the matrix P = A(ATA)-¹AT by itself. Cancel to prove that P² = P. Explain why P(Pb) always…

A: Here the Matrix . For this matrix P, .

Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: The given vectors are a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

Q: 1. Find A-C|(B – D) using the following vectors: A= C= D=

Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

Q: Find the value of k for which the vectors 4 4 -5 X = || = 4 and y = 0 1 -2 k are orthogonal.

Q: linearly independent If they are linearly dependent, find scalars that are not all zero s linearly…

Q: If u = and v = , find 1/3u - 2v. (this is a vector problem)

A: Given, u = < 3 , 9 > and v = < -3, 1 >,

Q: (a) Express the vector a × b in the form aa + 3b + yc, assuming that the vectors a, b and c are not…

A: a) Look care fully that we need to find the coefficients namely α,β,γ Determination of α:…

Q: Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

Q: Given -2 -81 A = 7 28 1 4 let aj be the first column vector of A, and a2 be the second column vector…

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

Q: Are the vectors ū = [4 -5 4], v = [2 2 -3] and w = [-1 -5 2] linearly independent? Choose If they…

A: To find Whether the given vectors are limearly independent or not.

Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…

Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

Q: If a = (4, 0, -1), find a vector b such that comp₂b = 3. b = X

A: a=<4,0,-1>ab=3ab=a→.b→a→let b=<b1,b2,b3>

Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

Question

(4) Find a least-square solution of Ax = b by finding orthogonal projection of b to ColA, where
)
()
1
5
4
A =
3
1
and
b =
-2
-2
4
-3
(Note that the column vectors of A are orthogonal.)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Determinant$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

4) Find a vector perpendicular to both i - 3j + 2k and 5i-j-4k. 5) Find the values of 2 that such that the given equations have non-
5. Show that the vectors a = 3i-j+ 4k, b =i-3j-2k and e = 4i– 3j+2k are linearly independent. Find numbers a, B and y such that d = 2i + 3j – k can be expressed in the form d= aa + Bb + 7c.
Let x, y, z be (non-zero) vectors and suppose that z = -1x + 1y and w = −1x + 1y - 3z. Are the following statements true or false?
If A= (3/2) i -(½) j + k and B= i+j+2k, what is the value of A x B? Are the vectors orthogonal? -2i-2j+2k, not orthogonal O -2i-2j+2k, orthogonal O 2i+2j-2k, not orthogonal
How do I solve this in steps?
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.
There are 6 linearly independent vectors in R5. O True False
Given the following vectors A = 4a +3a - 2a y B=a + 5a +7a_ X y C=-2a-4a +6a X y Evaluate |AX (BXC)|
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.
One of the following vectors lies in span{ 2+ x + x², 2x2} (A) 2+ 2x + 7x? (B) 2 + 2x + 5x? (C) 2 + 2x + 6x? (D) 2 + 2.x + 8x? (E) 2 + 2x + 9x2