Let Mn(R) be the set of n x n matrices with real entries. Define the sets V1 = {A € M2(R) | A = A"} V2 = {A € M2(R) | det(A) = 1} For both sets, show whether or not it (i) is closed under addition, (ii) is closed under real scalar multiplication,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let Mn(R) be the set of n x n matrices with real entries. Define the sets
Vị = {A € M2(R) | A = AT}
V2 = {A € M2(R) | det(A) = 1}
For both sets, show whether or not it
(i) is closed under addition,
(ii) is closed under real scalar multiplication,
1
(iii) contains an additive identity (zero vector),
(iv) contains the additive inverse of each of its elements.
Transcribed Image Text:Let Mn(R) be the set of n x n matrices with real entries. Define the sets Vị = {A € M2(R) | A = AT} V2 = {A € M2(R) | det(A) = 1} For both sets, show whether or not it (i) is closed under addition, (ii) is closed under real scalar multiplication, 1 (iii) contains an additive identity (zero vector), (iv) contains the additive inverse of each of its elements.
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