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Suppose we have the following two bases for R²:

Suppose we have the following two bases for R²:

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 31E
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I. Suppose we have the following two bases for R²: B = ( [;]-[;) ) and D = Let i = Find Repz() and Repp(). Repz(5) = Repp(i) = Find RepBp(id), the Change of Basis matrix from R, to Rž . Use that Change of Basis matrix to find Repp(i). Compare your answer with the one you obtained at the beginning of the problem. Repp (3) = Now, consider the standard basis ɛz for R2. Rep:, (1¿), Repe, ([})) Repez Let B = and D = Write down the bases B and D: Let B = and D= Create an augmented matrix by writing down the vectors in basis B and the vectors in basis D like this: [ D| B ]. Row reduce this matrix until you get the identity matrix on the left-hand side [D| B] → [ L[ ?? ]. What do you notice about the matrix you obtained on the right-hand side? THEOREM: Let B = (B, ..,Ba) and D = (51, ... , ốn), be bases for vector space V. Let B = (Repe(B1), ..., Repe(Bn)) and D = (Repc(51),...,Repc(5n)) where C is any basis of V. Then row reduce on the following augmented matrix yields [DI B] → [ 4| Repap(id) ]
Transcribed Image Text:I. Suppose we have the following two bases for R²: B = ( [;]-[;) ) and D = Let i = Find Repz() and Repp(). Repz(5) = Repp(i) = Find RepBp(id), the Change of Basis matrix from R, to Rž . Use that Change of Basis matrix to find Repp(i). Compare your answer with the one you obtained at the beginning of the problem. Repp (3) = Now, consider the standard basis ɛz for R2. Rep:, (1¿), Repe, ([})) Repez Let B = and D = Write down the bases B and D: Let B = and D= Create an augmented matrix by writing down the vectors in basis B and the vectors in basis D like this: [ D| B ]. Row reduce this matrix until you get the identity matrix on the left-hand side [D| B] → [ L[ ?? ]. What do you notice about the matrix you obtained on the right-hand side? THEOREM: Let B = (B, ..,Ba) and D = (51, ... , ốn), be bases for vector space V. Let B = (Repe(B1), ..., Repe(Bn)) and D = (Repc(51),...,Repc(5n)) where C is any basis of V. Then row reduce on the following augmented matrix yields [DI B] → [ 4| Repap(id) ]
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