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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

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 69E: Find a basis for R2 that includes the vector (2,2).

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Question

=
Consider the vector space R² with the standard basis {e1
{v1 = (1, 1), V2
=
= (1, 0), e2 = (0, 1)} and a new basis
new basis.
(1,-1)}. a) Find the change of basis matrix from the standard basis to the
b) Express the vector w = (2, 3) in the new basis {V1, V2}.

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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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