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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).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 16AEXP
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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)
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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