Explanation Given: The vector B is, B = { ( 4 , 2 , − 4 ) , ( 6 , − 5 , − 6 ) , ( 2 , − 1 , 8 ) } . The vector B ′ is, B ′ = { ( 1 , 0 , 4 ) , ( 4 , 2 , 8 ) , ( 2 , 5 , − 2 ) } . The coordinate matrix [ x ] B is, [ x ] B ′ = [ 1 − 1 2 ] T . Approach: The steps to be followed are as follows, Step 1: Write the matrix [ B B ′ ] in the graphing calculator. Step 2: Now select the rref ( option. Step 3: Select the matrix A and press ENTER to obtain the final result in the form of [ I n P − 1 ] . Step 4 : Select Frac option to obtain the final result in fraction. Calculation: The vector B is { ( 4 , 2 , − 4 ) , ( 6 , − 5 , − 6 ) , ( 2 , − 1 , 8 ) } . The vector in matrix form is, B = [ 4 6 2 2 − 5 − 1 − 4 − 6 8 ] . The vector B ′ is { ( 1 , 0 , 4 ) , ( 4 , 2 , 8 ) , ( 2 , 5 , − 2 ) } . The vector in matrix form is, B ′ = [ 1 4 2 0 2 5 4 8 − 2 ] . Convert the matrix as [ B B ′ ] → [ I n P − 1 ] . Take [ B B ′ ] as, [ 4 6 2 1 4 2 2 − 5 − 1 0 2 5 − 4 − 6 8 4 8 − 2 ] . Now, to convert [ B B ′ ] in the form of [ I n P − 1 ] with the help of graphing calculator, Step 1: Write the matrix [ B B ′ ] in the graphing calculator as shown in the figure below, To determine (b) To find: The transition matrix from B ′ to B where B = { ( 4 , 2 , − 4 ) , ( 6 , − 5 , − 6 ) , ( 2 , − 1 , 8 ) } and B ′ = { ( 1 , 0 , 4 ) , ( 4 , 2 , 8 ) , ( 2 , 5 , − 2 ) } . To determine (c) To verify: The two transition matrices are inverses of each other. To determine (d) To find: The value of coordinate matrix [ x ] B where [ x ] B ′ = [ 1 − 1 2 ] T .

8th Edition

ISBN: 9780357156100

Author: Ron Larson

Publisher: Cengage Limited

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Chapter 4.7, Problem 41E

To determine

(a)

To find:

The transition matrix from B to B′ where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

To determine

(b)

To find:

The transition matrix from B′ to B where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

To determine

(c)

To verify:

The two transition matrices are inverses of each other.

To determine

(d)

To find:

The value of coordinate matrix [x]B where [x]B′=[1−12]T.

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Chapter 4.7, Problem 40E

Chapter 4.7, Problem 42E

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(a) To find: The transition matrix from B to B ′ where B = { ( 4 , 2 , − 4 ) , ( 6 , − 5 , − 6 ) , ( 2 , − 1 , 8 ) } and B ′ = { ( 1 , 0 , 4 ) , ( 4 , 2 , 8 ) , ( 2 , 5 , − 2 ) } .

Solution Summary: The author explains how to find the transition matrix from B to Bprime.

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(a)

To find:

The transition matrix from B to B′ where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

(b)

To find:

The transition matrix from B′ to B where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

(c)

To verify:

The two transition matrices are inverses of each other.

(d)

To find:

The value of coordinate matrix [x]B where [x]B′=[1−12]T.

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Chapter 4 Solutions

(a) To find: The transition matrix from B to B ′ where B = { ( 4 , 2 , − 4 ) , ( 6 , − 5 , − 6 ) , ( 2 , − 1 , 8 ) } and B ′ = { ( 1 , 0 , 4 ) , ( 4 , 2 , 8 ) , ( 2 , 5 , − 2 ) } .

Solution Summary: The author explains how to find the transition matrix from B to Bprime.

Concept explainers

Videos

(a) To find: The transition matrix from B to B′ where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

(b) To find: The transition matrix from B′ to B where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

(c) To verify: The two transition matrices are inverses of each other.

(d) To find: The value of coordinate matrix [x]B where [x]B′=[1−12]T.

Want to see the full answer?

Chapter 4 Solutions

(a)

To find:

The transition matrix from B to B′ where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

(b)

To find:

The transition matrix from B′ to B where B={(4,2,−4),(6,−5,−6),(2,−1,8)} and B′={(1,0,4),(4,2,8),(2,5,−2)}.

(c)

To verify:

The two transition matrices are inverses of each other.

(d)

To find:

The value of coordinate matrix [x]B where [x]B′=[1−12]T.