Explanation Given: Two bases B and B ′ for a vector space V and the matrix for A for the linear transformation T : V → V relative to B . Calculation: The matrices for a linear transformation relative to two different bases are shown in Figure-1 Figure-1 In this section A , A ′ , P and P − 1 represent the following four square matrices, From the figure-1, Matrix for T relative to B : A , Matrix for T relative to B : A , Transition matrix from to B ′ to B : P and Transition matrix from B to B ′ : P − 1 . From the figure-1, There are two ways to get from the coordinate matrix [ v ] B ' to the coordinate matrix [ T ( v ) ] B ' One way is direct, using the matrix A’ to obtain A To determine (b) To find: Whether two square matrices A and A ′ of order n are similar.

Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

8th Edition

ISBN: 9781337604925

Author: Ron Larson

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 6.4, Problem 40E

To determine

(a)

To explain:

The process to obtain coordinate matrix [T(v)]B' from the coordinate matrix [v]B'.

To determine

(b)

To find:

Whether two square matrices A and A′ of order n are similar.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 39E

Chapter 6.4, Problem 41E

Students have asked these similar questions

Assume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the above

Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the above

Let H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane. Select an Answer u = 3 1. -10 8-8 -2 ,v= 5 Select an Answer -2 u = 3 4 2. + 9 ,v= 6

Chapter 6 Solutions

Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Prob. 4E Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Finding an Image and a PreimageIn Exercises 1-8,...Ch. 6.1 - Linear TransformationsIn Exercises 9-22, determine...Ch. 6.1 - Linear TransformationsIn Exercises 9-22, determine...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

(a) To explain: The process to obtain coordinate matrix [ T ( v ) ] B ' from the coordinate matrix [ v ] B ' .

Solution Summary: The matrices for a linear transformation relative to two different bases are shown in Figure-1.

Videos

(a)

To explain:

The process to obtain coordinate matrix [T(v)]B' from the coordinate matrix [v]B'.

(b)

To find:

Whether two square matrices A and A′ of order n are similar.

Want to see the full answer?

Chapter 6 Solutions

(a) To explain: The process to obtain coordinate matrix [ T ( v ) ] B ' from the coordinate matrix [ v ] B ' .

Solution Summary: The matrices for a linear transformation relative to two different bases are shown in Figure-1.

Videos

(a) To explain: The process to obtain coordinate matrix [T(v)]B' from the coordinate matrix [v]B'.

(b) To find: Whether two square matrices A and A′ of order n are similar.

Want to see the full answer?

Chapter 6 Solutions

(a)

To explain:

The process to obtain coordinate matrix [T(v)]B' from the coordinate matrix [v]B'.

(b)

To find:

Whether two square matrices A and A′ of order n are similar.