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If (X– A)(B – C) = D where all matrices involved are invertible square matrices, then: (A) X = + A В -С (B) X = D(B – C)1 + A (C) X = A + (B – C)*D (D) X = (D + A)(B – C)1

If (X– A)(B – C) = D where all matrices involved are invertible square matrices, then: (A) X = + A В -С (B) X = D(B – C)1 + A (C) X = A + (B – C)*D (D) X = (D + A)(B – C)1

Advanced Engineering Mathematics
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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If (X– A)(B – C) = D where all matrices involved are invertible square matrices, then: D + A В -С (B) X = D(B – C)1 + A (C) X = A + (B – C)*D (А) X%— (D) X = (D + A)(B – C)² Which of the following statement is true? I. A matrix and its inverse are commutative with respect to multiplication. II. An identity matrix is singular. III. The determinant of a matrix and the determinant of its inverse, if it exists, are reciprocals. (A) I, only (C) I and II, only (B) |I and II, only (D) All I, II, and II Which one of the following equations is true for nxn matrices A, B, and C? (Assume all matrices involved are defined and invertible) (A) A(CB)1 = (AB²)c² (B) 2(AB)1 = A{(2B1) (C) (A + B)1 = B1+A1 (D) (В + C)'A %3D вА + С 1А For matrix A, A? = A. Which one of the following must be true? (A) A is invertible. (B) A is an identity matrix. (C) A is a zero matrix. (D) Either (B) or (C)
Transcribed Image Text:If (X– A)(B – C) = D where all matrices involved are invertible square matrices, then: D + A В -С (B) X = D(B – C)1 + A (C) X = A + (B – C)*D (А) X%— (D) X = (D + A)(B – C)² Which of the following statement is true? I. A matrix and its inverse are commutative with respect to multiplication. II. An identity matrix is singular. III. The determinant of a matrix and the determinant of its inverse, if it exists, are reciprocals. (A) I, only (C) I and II, only (B) |I and II, only (D) All I, II, and II Which one of the following equations is true for nxn matrices A, B, and C? (Assume all matrices involved are defined and invertible) (A) A(CB)1 = (AB²)c² (B) 2(AB)1 = A{(2B1) (C) (A + B)1 = B1+A1 (D) (В + C)'A %3D вА + С 1А For matrix A, A? = A. Which one of the following must be true? (A) A is invertible. (B) A is an identity matrix. (C) A is a zero matrix. (D) Either (B) or (C)
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