To prove: The formula ( A 1 A 2 A 3 ⋅ ⋅ ⋅ A n ) T = A n T ⋅ ⋅ ⋅ A 3 T A 2 T A 1 T is true assuming that A 1 , A 2 , A 3 , …, A n are matrices with sizes such that the multiplications are defined.

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Answer 1

Question

Chapter A, Problem 12E

To determine

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

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Find the perimeter and area

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

Answer 2

Question

Chapter A, Problem 12E

To determine

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

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Answer 3

Question

Chapter A, Problem 12E

To determine

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

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Answer 4

Question

Chapter A, Problem 12E

To determine

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

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Answer 5

Chapter A, Problem 12E

To determine

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

Answer 6

Chapter A, Problem 12E

To determine

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

Answer 7

Chapter A, Problem 12E

To determine

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. A - Using Mathematical Induction In Exercises 1-4, use...Ch. A - Prob. 2E Ch. A - Prob. 3E Ch. A - Prob. 4E Ch. A - Prob. 5E Ch. A - Prob. 6E Ch. A - Prob. 7E Ch. A - Prob. 8E Ch. A - Prob. 9E Ch. A - Prob. 10E

To prove: The formula ( A 1 A 2 A 3 ⋅ ⋅ ⋅ A n ) T = A n T ⋅ ⋅ ⋅ A 3 T A 2 T A 1 T is true assuming that A 1 , A 2 , A 3 , …, A n are matrices with sizes such that the multiplications are defined.

Solution Summary: The author explains how to prove a formula for every positive integer n using mathematical induction.

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To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

Want to see the full answer?

Chapter A Solutions

To prove: The formula ( A 1 A 2 A 3 ⋅ ⋅ ⋅ A n ) T = A n T ⋅ ⋅ ⋅ A 3 T A 2 T A 1 T is true assuming that A 1 , A 2 , A 3 , …, A n are matrices with sizes such that the multiplications are defined.

Solution Summary: The author explains how to prove a formula for every positive integer n using mathematical induction.

Videos

To prove: The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.

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Chapter A Solutions

To prove:

The formula (A1A2A3⋅⋅⋅An)T=AnT⋅⋅⋅A3TA2TA1T is true assuming that A1, A2, A3, …, An are matrices with sizes such that the multiplications are defined.