Let A = (ajj), B (bij), C = (Cij) be real n × n matri- ces, where B = CT, Cij is the cofactor of the element aij, for all i = 1, 2, 3,...,n and j = 1, 2, 3, · · n. In other words, C is the cofactor matrix of A and B is the adjoint matrix of A. " Let λ, a, ß, y be real constants. 1. Which of the following statements is NOT true? = n (A) Σaik Cik = det (A) k=1 n (B) (C) (D) k=1 n k=1 n k=1 akjCkj = det (A) aikCjk det(A), i ‡j akiCkj=0,i # j (D) B 2. Which of the following statements is NOT true? (A) AB=BA = [det(A)]I (B) AC = CA = [det(A)]I B (C) A-¹ = = det(A) A det (A) where det (A) 0 in (C) and (D).
Let A = (ajj), B (bij), C = (Cij) be real n × n matri- ces, where B = CT, Cij is the cofactor of the element aij, for all i = 1, 2, 3,...,n and j = 1, 2, 3, · · n. In other words, C is the cofactor matrix of A and B is the adjoint matrix of A. " Let λ, a, ß, y be real constants. 1. Which of the following statements is NOT true? = n (A) Σaik Cik = det (A) k=1 n (B) (C) (D) k=1 n k=1 n k=1 akjCkj = det (A) aikCjk det(A), i ‡j akiCkj=0,i # j (D) B 2. Which of the following statements is NOT true? (A) AB=BA = [det(A)]I (B) AC = CA = [det(A)]I B (C) A-¹ = = det(A) A det (A) where det (A) 0 in (C) and (D).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Must solve the entire question. Don't solve it partially.
![Let A =
(ajj), B
(bij), C = (Cij) be real n × n matri-
ces, where B = CT, Cij is the cofactor of the element aij, for all
i = 1, 2, 3,...,n and j = 1, 2, 3, · · n. In other words, C is the
cofactor matrix of A and B is the adjoint matrix of A.
"
Let λ, a, ß, y be real constants.
1. Which of the following statements is NOT true?
=
n
(A) Σaik Cik = det (A)
k=1
n
(B)
akjCkj= det(A)
(C)
(D)
k=1
n
k=1
n
aikCjk det(A), i ‡ j
k=1
ΣakiCkj = 0, i j
=
2. Which of the following statements is NOT true?
(A) AB=BA = [det(A)]I
(B)
AC = CA = [det(A)]I
B
(C)
A-¹
(D) B
where det (A) 0 in (C) and (D).
=
det(A)
A
det(A)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda1c3e88-9a5c-4e68-9367-a15e4fbc2f2c%2Fee67324d-d6e4-4b58-8e92-25b6a84f00fe%2Fh4xvgqo_processed.png&w=3840&q=75)
Transcribed Image Text:Let A =
(ajj), B
(bij), C = (Cij) be real n × n matri-
ces, where B = CT, Cij is the cofactor of the element aij, for all
i = 1, 2, 3,...,n and j = 1, 2, 3, · · n. In other words, C is the
cofactor matrix of A and B is the adjoint matrix of A.
"
Let λ, a, ß, y be real constants.
1. Which of the following statements is NOT true?
=
n
(A) Σaik Cik = det (A)
k=1
n
(B)
akjCkj= det(A)
(C)
(D)
k=1
n
k=1
n
aikCjk det(A), i ‡ j
k=1
ΣakiCkj = 0, i j
=
2. Which of the following statements is NOT true?
(A) AB=BA = [det(A)]I
(B)
AC = CA = [det(A)]I
B
(C)
A-¹
(D) B
where det (A) 0 in (C) and (D).
=
det(A)
A
det(A)
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