Theorem: If P is the transition matrix from a basis B' to a basis B, then P is invertible and the transition matrix from B' to B is given by P-¹ and this can be found using Gauss-Jordan elimination as follows [B' | B] -> [P-¹]. Use the theorem above to find the transition matrix P(-1) from B to B' where B={(1,0),(1,-1)} and B'={(1,1),(1,-1)}.

Theorem: If P is the transition matrix from a basis B' to a basis B, then P is invertible and the transition matrix from B' to B is given by P-¹ and this can be found using Gauss-Jordan elimination as follows [B' | B] -> [P-¹]. Use the theorem above to find the transition matrix P(-1) from B to B' where B={(1,0),(1,-1)} and B'={(1,1),(1,-1)}.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.2: Diagonalization

Problem 45E

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Similar questions

Use the Gram-Schmidt orthonormalization process to find an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[022202220].
Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use c=3 in the expansion matrix and c=1 in the shear matrix. T1=[1001] Reflection in yaxis T2=[100c] Expansion or contraction in ydirection T3=[10c1] Shear in ydirection
a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving that if A is an nn symmetric matrix with positive eigenvalues, then there exists a symmetric matrix B such that B2=A.

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