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Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 71E

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Need help with this algebra question

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3
BB 80
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Your vectors are not orthonormal (or you may need to enter more decimal places)
Find an orthonormal basis of the plane x₁
6x2 x3 = 0.
1
0
1
3
1
-3

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Find a basis for R2 that includes the vector (2,2).
You are given the following vectors in terms of their components in the i, j, k basis: A = 11+1j+2k B = 11+-1j+2k C=0i+1j+-1k Use this set of vectors to construct a set of orthonormal basis vectors. To enter unit vectors, select "Vectors" on the PhysPad that opens when you click on the answer box. Select the "hat" and enter i, j, or k in the provided space using the buttons on the PhysPad. Once entered, you have to hit the right-arrow key or tab to move the cursor out from under the hat. If you do it incorrectly you will see the hat out of position over the vector. Please review your answer before submission. Take the first vector to be in the direction of A. V₁ = Take the second vector to be in the A-B plane. V₂ = 1 + 2/ V3 = i + 0} − k - √5 31 The third vector should be perpendicular to the A-B plane in a right-handed sense.
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Hi I got these wrong. Please help
show two nonzero vectors a and b in the 5th dimensions. put them in vector form and in basis form. Also find a unit vector in the direction of b.
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n-{() ()}} - {}) 0 )} 12 2 3 B = 3 23 B2 1 3 21 2 2 {)0 ( B3 = B4 4 1 3 -2 a-{() 0} --{) 00} 3 2 B5 B6 = 1 1 2
Find the vector X (in standard coordinates) determined by the given coordinate vector [X] B and the given basis B. 3 -2 {³}]} =[3³] B - 5 Enter the answer only (don't type your work here), using the equation editor. B =
Calculate the cross product. (5i - 9j+7k) x (i+j-7k) = ai + bj + ck (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) (a, b, c) =
Find an orthonormal basis of the plane x₁ +4x2x3 = 0.
Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate vector relative to the basis B is [X]B=(4, 5). (Write your answer in the form (a, b) where a and b are real numbers.)
Is this orthonormal or just orthogonal? I thought you needed to normalize the vectors (i.e. divide them by their lengths to make them unit vectors) in order to make it an orthonormal basis. Did I make a mistake?

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