2. Problem 2 Let A = 2 1 -1 1 -3 -1 1 0 1 1 " W = col(A), and x = 3 -4 -1 2 (a) Find Projw(x). (b) Construct bases for W and Null(AT) and verify that every vector in basis for W is orthogonal to every vector in a basis in Null(AT). (c) Use the Gram-Schmidt process to find an orthogonal basis for W.

2. Problem 2 Let A = 2 1 -1 1 -3 -1 1 0 1 1 " W = col(A), and x = 3 -4 -1 2 (a) Find Projw(x). (b) Construct bases for W and Null(AT) and verify that every vector in basis for W is orthogonal to every vector in a basis in Null(AT). (c) Use the Gram-Schmidt process to find an orthogonal basis for W.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...

See similar textbooks

Related questions

Q: . Consider the following non-linear system of differential equations x'=xy- 2, y = x - 2y. Note that…

Q: The graph of f(t) is given below. 765 4 7₁ 6 5 y 3₁ 2 1 t o 10 Find the Laplace transform F(s) =…

A: The given graph has 4 stages. First stage: for Second stage: The…

Q: (14) Let G be a finite cyclic group of order n with identity element e. Prove that if a € G, then cd…

A: The order of every subgroup of a finite group G is divisor of the order of G.

Q: 8. A vector field F is given in cylindrical polar coordinates by F(p₁6, 2) == cos(7²)₂ Find the…

Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

Q: given the function determines: a) maximum and minimum points b) intervals where the function…

Q: Part II. Writing the equation d² dt2 in the form of the system d dt X = U, X = x³ + x², x = x(t), dv…

A: Let md2dt2x=F(x) be a differential equation, then the conservative quantity is given by…

Q: Find a linearization of the differential equation for x near 0.

A: Given data from the problem are :

Q: For each of the following vector fields F, decide whether it is conservative or not by computing the…

Q: Find the standard matrix for the linear transformation T: R² R² that reflects points about the line…

A: Linear Transformation T: R2 to R2 that ''reflect'' points about the line x2=x1Claim : find…

Q: Let T: P₁ → P₁ is a linear operator represented by MB(T): -2 1. suppose PD+B = . Find Mp(T). (88) =…

Q: Suppose a subspace is spanned by the set of vectors shown. ((-24].[23]) Find a basis for the…

Q: Use the information given about the angle 0, cos 0 = -- (a) sin (20) (b) cos (20) (c) sin (d) cos…

A: Using basic formulas in trignometry we solve this problem.

Q: In a mathematics competition, there are 10 multiple-choice questions. Each question has one correct…

A: The binomial probability formula is given by:P(X=k)=(nk)⋅pk⋅(1−p)n−kwhere:(nk) is the number of ways…

Q: 3. The behavior of the system is a spiral source. 3x + y, | y' = = -x + 4y x' =

Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

Q: You are holding one red sock. In your sock drawer are 4 blue socks, 2 green socks, 8 white socks,…

A: We are given that, in a socks drawer Number of blue socks = 4 Number of green socks = 2 Number of…

Q: 4. The Fibonacci numbers are defined as: f0 = 0 , f1 = 1 , and fn = fn−1 + fn−2 , for n ≥ 2 Provide…

A: Given, f0=0,f1=1 and fn=fn−1+fn−2,n≥2 .Let P(n) be the statement such that 3|f4n .That is,…

Q: (2) 1 x, 32 € Zunder matrix addition and mul- 0z tiplication and the ring S = Z x Z of Exercise 22…

A: 3. Consider the ring under matrix addition and multiplication and the ring .Determine whether ,…

Q: Give a basis for the image of the matrix A. 0 0 1 -2 A = 1 -1 2 −5 0 0 5 -10 Number of Vectors: 1…

Q: Find the product of the following matrices, if possible. :] [: -6 9-6 O A. Select the correct choice…

A: We use basic rules of matrix multiplication to solve this problem.

Q: Pick two random vectors in R³ (no zeros - few repeated numbers) and call them u and 7. Compute the…

Q: 2. Using the sequence z n, show that (R, d) is not a compact space. 3. Deduce.

A: A compact metric space is also sequentially compact metric space.Sequentially compact metric space…

Q: Part II. Writing the equation d² dt2 in the form of the system dx d dt (c) (d) (e) = V, = x³ + x², X…

A: To solve part(d) , we need part(a),(b),(c) , that's why I am solving first four parts.

Q: nt or A= Pert to solve. Use the compound interest formulas A = P1+. n 41) Find the accumulated value…

A: The given investment amount at compunded for years.The aim is to find the accumulated amount if…

Q: The payoff matrix and strategies P and Q (for the row and column players, respectively) are given.…

Q: 1. 2. The degree and leading coefficient of f(x) = -x + 3x² - 2x³ + 5 is a) degree of 1 with leading…

Q: Let I:= [a, b] and let f: I -> R be a continuous wetion such that f(x) >0 for each x iN I. Prove…

Q: Writing the equation d² dt2 n the form of the system dx x = V, =) 3) e) X= dt x³ + x², v = x³ + x² x…

Q: Use the divergence theorem to evaluate the surface integral missing z = 0, and N is the outward unit…

Q: 2. Let X₁, X2, and X3 be independent random variables such that E(X₁) 6 Further, suppose that V(X₁):…

A: Let X1, X2, and X3 be independent random variables. 1. We have to Compute E(eX1X2+πX2X3+√19X3+3)2.…

Q: Agriculture. Table 3 shows the yield (in bushels per acre) and the total production (in millions of…

A: Given information:Data on corn yield (bushels per acre) and total production (million bushels) for…

Q: The Folium of Descartes is an implicitly-defined curve, significant in the history of mathematics.…

Q: The sequence of numbers we’re generating are traditionally constructed like this: Start with the…

A: The sequence of numbers generated by the traditional procedure is called the Fibonacci…

Q: = Let R be the region in the first quadrant bounded by the lines y 1 hyperbolas xy = -2, xy = 2. and…

Q: Find the only possible solution to the nonlinear programming problem 2 max (400 - 5x²- 9y²) subject…

Q: Consider the following initial value problem. 0 1 ≤1 12 1 ≤ 1 < 6 0 6 ≤ 1< 00 y' + 3y = y(0) = 10…

A: The Laplace transform of a function f(t) is defined as L{f(t)}=∫0∞f(t)e−stdt .Formulas: (1)…

Q: (i) For what x-values is 300(1.1)* > 200(1.2)*? 300(1.1)* > 200(1.2)* when x Sv i (ii) For what…

A: We shall use the basic inequality of logarithms.

Q: Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid…

Q: Prove that C5 is isomorphic to its complement.

Q: 11. the interval 0 ≤t≤ 167. Find the curvature function and evaluate it at t = 7. Graph the curve…

Q: 2. Compute [fs xy dS, where S is the surface of the tetrahedron with sides z = 0, y=0, x+ z = 1 and…

A: We have to Compute ∫∫S xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x +…

Q: 7. 8. What is the horizontal asymptote of f(x) a) y = 2/1/20 b) y = = 3x+47 2x-1 c) y = 121/12 What…

Q: Suppose a subspace is spanned by the set S of vectors shown below. s={[G]-[-2.]} S Find a subset of…

Q: results for two possible side effects. A drug trial had 226 participants. A survey was done to…

A: The objective of the question is to understand the distribution of participants who experienced…

Q: I can't follow any of the writing. Some of it is dim, and some doesn't make sense: In the problem,…

A: One must not assume f(c)= 0.But If one assumes that , then the claim "" is true.

Q: 6. If the complex number -2+3i is an eigenvalue of a matrix A = a, b, c, d are real numbers, then…

Q: 11/6 is the wrong answer

Q: 2. The equation that models the amount of time, +, in minutes that a cup of hot chocolate has been…

A: Given that the equation that models the amount of the time, t in minutes that a cup of hot chocolate…

Q: The system of first order differential equations: has solution: y₁ (t) Y₂(t) - = Note: You must…

Question

answer for parts b and c

1 -3 0
-(---)
W = col (A), and x =
1
2. Problem 2 Let A =
2 1 1
-1
0
3
-4
2
(a) Find Projw(x).
(b) Construct bases for W and Null(AT) and verify that every vector in basis for W is
orthogonal to every vector in a basis in Null(A™).
(c) Use the Gram-Schmidt process to find an orthogonal basis for W.

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: Given information:

VIEW

Step 2: To find a basic for col(A) :

VIEW

Step 3: To find a basis for Null(A^T) :

VIEW

Step 4: Solve for X:

VIEW

Step 5: To find an inner product of each vector in W:

VIEW

Step 6: To find an inner product of each vector in W:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector space?
Find a basis for R2 that includes the vector (2,2).
Let v1=( 0 1 -1 2)^T v2=(1 0 -2 1)^T Let V=Span{v1,v2} Find a basis for the orthogonal complement of V.
Let B = {(1,1),(3,2)} and B′ = {(4,5),(2,4)} be two bases of R2. Let v be a vector with (v)B′ = (5, −6). E denotes a standard basis for R^2 (a) Based on the definition of coordinate vectors, compute v (in the standard basis) from the coordinate vector (v)B′ = (5, −6). (b) Find the transition matrix PB←B′ . (c) Use the transion matrix PB←B′ and (v)B′ = (5,−6) to find (v)B. (d) Based on the definition of coordinate vectors, compute v (in the standard basis) from the coordinate vector (v)B that you have obtained in part (c). Does it agree with your answer from part (a)? (e) Find the transition matrix PE←B′ . (f) Find the transition matrix PB←E. (g) Compute the product PB←E, PE←B′, and explain why the product equals to PB←B′ . I want anwers for part(d)(e)(f) and (g).
How can I find a basis for KerT of the attached function? I know that T is linear but how do I find the KerT and therefore the basis?
If f(x) = x^2 + 7x+2, g(x) = x^2 - x + 1 find a polynomial h(x) of degree 2 such that together these 3 are linearly independent Find constant c such that the three vectors (1,1,4),(2,1,1) and (7,5, c) DO NOT form a basis for 3d-space
(1) Let B = {√₁, 72, 73} be the basis of R³ defined by 1 *-(). *- (). *-(1) ), = = = Find the dual basis of B.
Let v1 -2 -3 v3}. Find the basis for H. = , v2 = 1 ' v3: = H 3 and the H = span{v1, v2,
4. Find a basis of each vector space below and hence write down the dimension of the space. You do not need to prove that your vectors form a basis. -{{:)-« ( :) ( 9) ( :) G 9). {(:)-* a a V1 Q³ : a V2 : E Q° :a+ 26 + c = 0 V3 = V4 = 1 2 -1
The vectors -6 01 = 02 = 03 =| 4 form a basis for R' if and only if k +
If the matrix of change of basis form the basis B to the basis B' is A= change of basis from B to B is: ● B. ~ (3) (-27). then the second column of the matrix of
20. (1) Give the coordinates of (4, 1, 5) in the basis (2) * Give the coordinates in the canonical basis of the point whose coordinates in the basis above are (3, 2,6) (3) Give the coordinates of (10, 3, 6) in the basis () 1 3