CHALLENGEACTIVITY7.4.1: Finding an orthogonal basis using the Gram-Schmidt process.469360.2546800.qx3zqy7Jump to level 120Let {U₁ = [ ²₁ 2], 0r = [-2₁ -18].[3]}U₂, U3=-18Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product.a{K₁ = [₁₂2] · M = [81] ₂ B =,-1-4Orthogonal basis:a = Ex: 5b = Ex: 5C = Ex: 1.23be a basis for a subspace of R2x2-1.59-1.65d = Ex: 1.23с3}

Answered: Image /qna-images/answer/965063ff-a32e-4c93-a623-93df1c88188e.jpg

Jump to level 1 Let (U₁=[2₁2] ₂-[-1818)-[3]} U3 = 0 Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basis: V₁ a = Ex: 5 b: 0 0 a 1.59 * {v₁ = [²₁₂2] ·M = [8 -¹8]. ³₁ = [1185 2]} V₂ V3 -1 -1.65 Ex: 5 0 C = Ex: 1.23 be a basis for a subspace of R2x2. d=Ex: 1.23

Jump to level 1 Let (U₁=[2₁2] ₂-[-1818)-[3]} U3 = 0 Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basis: V₁ a = Ex: 5 b: 0 0 a 1.59 * {v₁ = [²₁₂2] ·M = [8 -¹8]. ³₁ = [1185 2]} V₂ V3 -1 -1.65 Ex: 5 0 C = Ex: 1.23 be a basis for a subspace of R2x2. d=Ex: 1.23

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: Let R. be the Euler rotation matrix for the spin-1/2 system such after rotation by the R, the…

A: The given information in this question is that we have a spin-12 system and a spinor ∅=12,i2T The…

Q: Suppose the vectors u and v are a basis B for R^2 and T is a transformation from R^2 → R^2 that maps…

A: Hello. Since your question has multiple parts, we will solve the integration by first method for…

Q: Let = 3 -26 4 -{--8--[F]--A} 26 , = 52 , = find an orthogonal basis under the Euclidean inner…

A: For any query with the solution please ask in the comment box.

Q: 5. Consider the basis B = {(3,2), (1,-4)} for R². Use the Gram-Schmidt process to rewrite this basis…

A: Using Gram Schmidt process we can find the orthonormal basis.

Q: The Gram-Schmidt process t ransforms the basis u-3,1), u23D(7,1) of R into the orthogonal basis…

A: First option is correct answer. Thankyou !

Q: Using (X,Y)= tr(XYT) as the inner product of M22, apply Gram-Schmidt Orthogonalization Algorithm to…

A: Given basis Finding the orthogonal basis

Q: Prob 1. Let U:= {pe P₂ (R): f₁(xp" (x) + p'(x)) dx = 0}. (a) Find a basis for U. (b) Extend your…

A: Let (a) We have to find a basis of Let be an arbitrary element of Then, Now, Then,…

Q: √6 -2√6 0 √6 -2 √4 3√3 1 √4 3√3 √4 √3 √4 3√3 -2 -1 1 (800)} 1 1 3 * * * * * * * 3√3 2

Q: (1x30'+ 3xD+1)y:о, усідів, у'(1)-о утобу'+0.09у= y (0) = 2.2, y' (0) = 0.14 -0.3x -o-3x e хе

Q: Select all that constitute a basis of solutions for the following by the Frobenius method x²y" + 6xy…

A: Given differential equation isx2y″+6xy′+(4x2+6)y=0Rewrite the equation asy″+6xy′+4x2+6x2y=0Here…

Q: 1 0 Let {U₁ = [¹, 2] · ₂ = [° 8] ³4 = []} ₁ , U2 , U3 Gram-Schmidt process to find an orthogonal…

Q: By the Gram-Schmidt process, obtain an orthonormal basis for R³ from the ordered basis given by…

A: The given vectors,Using the Gram-Schmidt orthogonalization we have to find an orthonormal basis for…

Q: Let {U₂₁ = [2 - ₁] ₁ U₂ = [0 12], 4]} the Gram-Schmidt process to find an orthogonal basis under the…

Q: After applying the Gram-Schmidt Orthonormalization Process to the basis 1 В 4 2 we get the basis a 1…

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: Question 4 (a) Let T:R'→R' and a {e.e,.e,,e}. be the standard basis of R' and B={v,v,,v,} is some…

A: Note that, here the elements are row vectors operate from left side,

Q: -80 20 []} 60 find an orthogonal basis under the Euclidean inner product. Let U₁ = 4 Orthogonal…

Q: How can I find [L] from basis B to basis C, if basis B = {1 + x + x^2, 1 + x, 2x + x^2} and basis C…

Q: let R3 have the Euclidean inner product and use the Gram-Schmidt process to transform the basis…

Q: Consider the vectors u (a) Show that 8= (, z, s} is an orthogonal hasis for R", and eompute |u . (b)…

Q: (1) Let Vi 3D (1,-1, 1), Vz — (-1,1, -4), Vз — (4, -2, -3). Apply the Gram-Schmidt orthogonalization…

A: Orthonormal basis

Q: = 6 | [1 0 , E12 Eu = 8 En = 8 . and En = 7. Let E11 and E22 Use the {E11, E12, E21, E22} is a basis…

A: That's easy. Have a great day!!!

Q: Consider the following two bases of R: {(E) () 0} {{:) () B = C = 4 What is the change-of-basis…

A: The base change from B to C is given by = B-1C

Q: Suppose V = P2 with the inner product p(x)q(x)a Apply the Gram-Schmidt orthogonalization process to…

Q: 1 2 -1 1 (VI). (12' ) Let A=| 0 2 -1 0 Find a basis for the row space of A and a 1 4 -2 1 basis for…

A: Answer and explanation is given below..

Q: Consider the vectors in C? (sometimes called spinors) ' (cos(0/2)e-ie/2 sin(0/2)e-i+/2 -…

Q: 6. Prove that the Rotation Matrix R corresponding to quaternion q = (a, b, c, d) is given by 1. R=…

A: Hint: Consider a 3×3 matrix a00a01a02a10a11a12a20a21a22

Q: On P(R), consider the inner product given by 1 (p · q) = ["'p(x)q(x) dx. Apply the Gram-Schmidt…

A: Given inner product is Let Using Gram Schmidt Process to make orthogonal. Let Using Gram Schmidt…

Question

CHALLENGE
ACTIVITY
7.4.1: Finding an orthogonal basis using the Gram-Schmidt process.
469360.2546800.qx3zqy7
Jump to level 1
2
0
Let {U₁ = [ ²₁ 2], 0r = [-2₁ -18].[3]}
U₂
, U3
=
-18
Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product.
a
{K₁ = [₁₂2] · M = [81] ₂ B =
,
-1
-4
Orthogonal basis:
a = Ex: 5
b = Ex: 5
C = Ex: 1.23
be a basis for a subspace of R2x2-
1.59
-1.65
d = Ex: 1.23
с
3}

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: Find V_1 and V_2

VIEW

Step 3: Find V_3 and a,b,c and d

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

469360.2546800.qx3zqy7
Jump to level 1
20
0
-2
3
Let
{ " = [ 2² ] ₁0 - [18] - [1 2]}
=
U₁
,U₂
, U3
-2
16
0
the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product.
Orthogonal basis: V₁
a = Ex: 5
a
= {v₁ -[-²8] ·½ - [8 8]·²-[-0.67 2]}
= |
V₂ =
=
b=
||
Ex: 5
C = Ex: 1.23
d=
be a basis for a subspace of R2x2. Use
=
Ex: 1.23
2
3
5

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

V =R * R 10a6b T(") - (170-100) {(2)· (3)} B = { find the matrix representation of T with respect to beta. Then determine wether beta is a basis consisting of eigenvectors. I have got -2 [T]₁ = ( 2 4 this does not match answer key. What's wrong? please point it out and have the rest of solution to the problem. thanks!
Question 13 of 13 -/1 Let Rª have the Euclidean inner product. Use the Gram-Schmidt process to transform the basis {u1, u2, U3, U4, } into an orthonormal basis. U1= (0,2,1,0), u2 = (1, – 1,0,0), u3 = (1,2,0, – 1), u4 = (3,0,0,3) %3D %3D %3D 1 1 1 5 1 5 2 5 65V 6 5 91 = 92 = 5 1 5 2 |5 5 1 5 2 5 93 = Võ3 V 6 5V6 ). 4 = 5 1 4 2 5 V6'5 6 1 1 %D 92 I| 9^ 9^ 9^ 51 5 2 6' 3 ▼ 6'5 V 6 5 1 5 2 5 6' 5 V 6'5V 6' 93 4 %D 94 = 152 5V6 5 1 1 92 5 5 152 1 6' 5 6'5V6 5 1 5 2 [5 93 = 94 = 3 V6 51 1 5 2 5 5 92 = 65V 91 0, V5' V5 2 3 (tVtV - V - V). 94 = %3D 93 V15' V15 V15 V15
Let S = = span {x¹ = x3 4 (a) Use Gram-Schmidt process to find an orthogonal basis {u¹, u², u³} of S. (b) Find an orthonormal basis {q¹, q², q³} of S.
[ 5/4 -3/4] -3/4 5/4. Let A write A UAU-1 where U is unitary, columns are orthonormal basis for R? and A = with A1 > A2. Recall: U-1 = UT for unitary U.
Find w if (w)s= W = [] -11 1 ΓΟΤ relative to the basis S = {3 3 " 1 1 ' 3 }
(2, 4, 0), the Gram-Schmidt process Given vị = (-1, 2, –1), v2 = (1, 7,1) and v3 allows us to construct an orthonormal basis {u1, u2, U3 } of R³ such that u¡ is a multiple of V1, u2 is a linear combination of vj and v2, and uz is a linear combination of v1, V2 and v3. Then u2 is equal to: O (1,1, 1) O (1,2, 0) (1:2'0뚜 이 O (0, 1, 0) o (-1, 2, –1) ㅇ 늘(1,0, 1)
Help
[4 -1 6] Given that 2 is an eigenvalue for A = |2 [2 1 Find a basis of its -1 8 Eigen space.
The set -23 (-0-0-0-0) 16 is a basis for R Use the Gram-Schmict process to produce an orthogonal basis for ¹. 111 = V₁ = U₂ = V₂ 11 VJ -15 -3 your answer" 11₁ = V₁ U₂ V₂. 11111 To make computations nice, if necessary, we can scale this vector by a non-zero scalar, so that y= ū₁ = us -U₁= 11V₂ HH 11₁ all To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u₂ = ₂ Va 1₂ U₂ u₂ V4. u₁u₂ 1₁ (Do not scale your answer -= -u₂ = 11₂ 11 (Do not scale r (Do not scale your answer) To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that Therefore, [u, uz, us. u) is en orthogonal basis for R. To obtain an orthorormal basis, we scale each of these vectors as follows: Û₂ = u;= 3 1 113 VI 113 113 -1₂ = |u₁|| -1₂ = Note: To enter a number of the form type a/sqrt(n) Thus, (₁, ₂, 3, 4) is an orthonormal. basis for R 113= -6 -6 -15
Let + {U₁ = [₁ ], U₂₁ = [2₂8] · U₂ = [-2² , U3 20 Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basis: V₁ a = Ex: 5 =[]} a 2 {v₁ = [1₂8], v₂ = [8²], b = Ex: 5 3], V₁ = [1 V3 c = Ex: 1.23 -1.33 1.33 be a basis for a subspace of R2x2. Use the d= a]} Ex: 1.23
Find a basis for p.
1 3. (а) Find an orthonormal basis B {ū1, ū2, đ3} of R³ such that u and the x-component of ūz is 1/3. [1 Find the coordinate vector of 3 relative to the basis B. (b) 1