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Let A be a fixed 10 x 10 matrix and let H be the set of all 10 x 10 matrices N with the property that NT A = A N. That is, H = {N | NT A = AN}. Is H a subspace of all 10 × 10 matrices? Justify your answer. Reminder: (A + B) = A + BT and (CA) = c (AT)

Let A be a fixed 10 x 10 matrix and let H be the set of all 10 x 10 matrices N with the property that NT A = A N. That is, H = {N | NT A = AN}. Is H a subspace of all 10 × 10 matrices? Justify your answer. Reminder: (A + B) = A + BT and (CA) = c (AT)

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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Let A be a fixed 10 x 10 matrix and let H be the set of all 10 x 10 matrices N with the property that NT A = A N. That is, H = {N | NT A = AN}. Is H a subspace of all 10 x 10 matrices? Justify your answer. Reminder: (A + B) = A + BT and (CA) = c (AT)
Transcribed Image Text:Let A be a fixed 10 x 10 matrix and let H be the set of all 10 x 10 matrices N with the property that NT A = A N. That is, H = {N | NT A = AN}. Is H a subspace of all 10 x 10 matrices? Justify your answer. Reminder: (A + B) = A + BT and (CA) = c (AT)
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