Solved: True or False? In Exercises 55 and 56, determine whether each statement is true

Chapter 4, Problem 55

(choose chapter or problem)

In Exercises 55 and 56, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) If P is the transition matrix from a basis B to \(B^{\prime}\), then the equation \(P[\mathbf{x}]_{B^{\prime}}=[\mathbf{x}]_{B}\) represents the change of basis from B to \(B^[\prime}\).

(b) If B is the standard basis in \(R^{n}\), then the transition matrix from B to \(B^{prime}\) is \(P^{-1}=\left(B^{\prime}\right)^{-1}\).

(c) For any 4 × 1 matrix X, the coordinate matrix \([X]_{S}\) relative to the standard basis for \(M_{4,1}\) is equal to X itself.

Text Transcription:

B^prime

P[mathbf x]_B^prime =[mathbf x]_B

B^prime

R^n

B^prime

P^-1 =(B^prime)^-1

[X]_S

M_4,1