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If C is a real square matrix, then C² + I (I is the identity matrix ) is non-singular. - The vector spaces U = {M e R³×3 : M = MT} and V = {N € R3×3 : the sum of the entries in each row of N is equal to 0} are isomorphic.

If C is a real square matrix, then C² + I (I is the identity matrix ) is non-singular. - The vector spaces U = {M e R³×3 : M = MT} and V = {N € R3×3 : the sum of the entries in each row of N is equal to 0} are isomorphic.

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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Prove or disprove question d.

(c) If C is a real square matrix, then C2 + I (I is the identity matrix ) is non-singular. (d) The vector spaces U = {M € R³×3 : M = MT} and V = {N E R3x3 : the sum of the entries in each row of N is equal to 0} are isomorphic.
Transcribed Image Text:(c) If C is a real square matrix, then C2 + I (I is the identity matrix ) is non-singular. (d) The vector spaces U = {M € R³×3 : M = MT} and V = {N E R3x3 : the sum of the entries in each row of N is equal to 0} are isomorphic.
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