The following restrictions are required for each problem: No matrix A, B, or C can be diagonal, none can be equal or a scalar multiple of each other, and no product can be the zero matrix (except (d)) or scalar multiple of the identity matrix (except (e)). All of the below are possible with these restrictions. (а) АВ BA but neither A nor B is 0 nor I, and A + B. (b) АВ # BА. (c) AB = AC but B # C, and the matrix A has no zeros entries. (d) AB = 0 but neither A nor B is 0. (e) AB = I but neither A nor B is I.
The following restrictions are required for each problem: No matrix A, B, or C can be diagonal, none can be equal or a scalar multiple of each other, and no product can be the zero matrix (except (d)) or scalar multiple of the identity matrix (except (e)). All of the below are possible with these restrictions. (а) АВ BA but neither A nor B is 0 nor I, and A + B. (b) АВ # BА. (c) AB = AC but B # C, and the matrix A has no zeros entries. (d) AB = 0 but neither A nor B is 0. (e) AB = I but neither A nor B is I.
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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I have attached the picture, please see the restrictions.
Transcribed Image Text:The following restrictions are required for each problem:
No matrix A, B, or C can be diagonal, none can be equal or a scalar multiple of each other,
and no product can be the zero matrix (except (d)) or scalar multiple of the identity matrix
(except (e). All of the below are possible with these restrictions.
(a) AB = BA but neither A nor B is 0 nor I, and A 7 B.
(b) АВ 2 ВА.
(c) AB = AC but B # C, and the matrix A has no zeros entries.
(d) AB = 0 but neither A nor B is 0.
(e) AB = I but neither A nor B is I.
Fool: 6:
MATI AR
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ont in ConvoG
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