Let L: R2 R2 be defined by L 4*]-[***] represents the coordinates of v in the standard ordered basis. A = ↓ 1 •{[:] [:) Using the standard ordered basis find a matrix A such that [L(x)] = A[x] for all x E R2. Here, given a vector v, [v]

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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Let L: R² R2 be defined by L
4]-[***]
=
x2
X1
represents the coordinates of v in the standard ordered basis.
A =
↓ ↑
{:] [:)}-
find a matrix A such that [L(x)] = A[x] for all x € R². Here, given a vector v, [v]
I
Using the standard ordered basis
Transcribed Image Text:+ Let L: R² R2 be defined by L 4]-[***] = x2 X1 represents the coordinates of v in the standard ordered basis. A = ↓ ↑ {:] [:)}- find a matrix A such that [L(x)] = A[x] for all x € R². Here, given a vector v, [v] I Using the standard ordered basis
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