Let a. Find the orthogonal projection of bonto Col(A). 34 21 projcol (A) (5) 1 2 +49-8 A = -2 1 b = 0 -10 = 130 21 124 21 X b. Find a least-squares solution, , of Az = b. 2 6

Q: 1. If A = find A1000 by diagonalizing. )Show every single step for your work).

A:

Q: ✓3.10 Project the vectors into M along N. {(*) Ix+y=0}, (b) (¹). (c) M={ M={ '(^).. () () N = {…

A:

Q: 3. Consider the statements below. (I) For each b in Rnı the equation Ax = b has a solution. (II)…

A:

Q: Find linearly independent vectors which generate al lutions of Ax = 0.

A:

Q: Let u = (1, 0, 2), v = (0, 1, 1) and w = (2,1,0). Which of the following statements are true? (i)…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Qn 1. Consider the following six points in R²: Aj — (1,0), Аз— (3,0), Аз- (2, V3), В, — (0,3), В, —…

A: Given the following six points in ℝ2. A1=(1,0), A2=(3,0) , A3=(2,3) , B1=(0,3) , B2=(3,2), B3=(0,1)…

Q: Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. A= 01…

A: Column space, Col A is a subspace spanned by columns of the matrix A.Let {u1,u2,⋯,ur} be an…

Q: 2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your…

A:

Q: 4

A: We are given the following vectors.

Q: Consider the vectors U₁ = 2x² + 2x - 1 and U₂ = -x² - 3x + 1 in P₂. Which of the following vectors…

A: Vectors v1=2x2+x-1 and v2=-x2-3x+1. To find the vectors that are linear combination of v1 and v2.

Q: Let A = Q1R1 = Q2R2, where Q1 and Q2 are orthogonaland R1 and R2 are both upper triangular…

A: Since A = Q1R1 = Q2R2, we can write:   Q2^TQ1R1 = R2   Since Q1 and Q2 are orthogonal, their product…

Q: -2 -5 8 0 -171 3 -5 1 1 A = 3 11 -19 7 1 1 7 -13 -3

A:

Q: Please don't provide handwritten solution ..

A: Please comment down for any doubt. I hope my answer helps you.

Q: Let a = (2, – 3, – 1) and b = (– 5, – 1, k). %3D %3D - Find k so that a and b will be orthogonal.…

A: Since we have been given that a⇀ = <2, -3, -1> and b⇀ = <-5, -1, k>Our aim is to find…

Q: Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. A =…

A:

Q: (1-3) symmihic from of the line find its general frm. 7,& . A180 pas allel eY

A: Equation of the given lines are,π1=2x-y+z=6 and π2=x+y+2z=3

Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: In the diagram below ABGH, BCFG and CDEF are squares. Prove that 21 + 2 = Z3. A В C D <4 <6 <5. <7…

A: GF/DF =1/√2 FD/FH=√2/2 = 1/√2 So, ∆GFD~ ∆ DFH Angle 1= angle 6

Q: Suppose u, v and w are non-zero vectors in R" such that proj(-2v) a and proj(5w)= b. Use the…

A: Projection vector of a→ in the direction of b→ Proj b→a→= a→.b→b→×b^=a→.b→b→b→2

Q: Show that if PER"×" is an orthogonal projector, then P+ = P.

A:

Q: Use the Row Reduction Algorithm to solve the following. Describe the solution set of Ax=b in the…

A: Given system of linear equations:Ax=bWhere A=[3−377164−491022−11−2−3−5]  ,  b=[−24−355]The augmented…

Q: 3. Use perfect squares or difference of squares formulas: a) (V5b – 8)? = b) 36x2 — у2 %3D - c) (2w²…

A:

Q: Let a = (1, – 5, 3) and b = ( – 5, 3, k). | Find k so that a and b will be orthogonal. k =

A: a→=1,-5,3b→=-5,3,k To find: value of k for which both will be orthogonal.

Q: The dot product of two vectors can be written in the form s+ 18 t. x1 x2 in R" is defined by * ·ý =…

A:

Q: Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 1 4…

A:

Q: The vectors V= 5 El 6 -17 u= are linearly independent if and only if k 4 8 -5+k , and w = 2 8 -18

A:

Q: Compute the orthogonal projection of u onto v. Use the square root symbol '' where needed to give an…

A:

Q: 3.10. Rotate the vectors by 30%. *:[],三闾

A: We have to Rotate the given vectors by 30°.

Q: I! the columns ola7*7 matnix D what Can be said abaut linearly independent , the solutions of DX = b…

A: Let D is a 7 x 7 matrix whose column are linearly independent. Since all columns are linearly…