b. For each of the following sets, either show that the set is a vector space or
ID: 2945140 • Letter: B
Question
b. For each of the following sets, either show that the set is a vector space or explain why it is not a vector space.
+ The set R of real numbers under the usual operations of addition and multiplacation.
+ The set {(x,0)¦x € R} under the usual operations of addition and multiplacation on R^2
+ The set {(x,1)¦x € R} under the usual operations of addition and multiplacation on R^2
+The set {(x,0) ¦x € R, x=0} under the usual operations of addition and multiplacation on R^2
+The set {(x,1) ¦x € R, x=0} under the usual operations of addition and multiplacation on R^2
+The set { [ a a+b] }
{ [ a+b a ] ¦a,b € R } under the usual operations of addition and multiplacation on R^2×2
+The set { [a a+b+1] }
{ [a+b a ] ¦a,b € R} under the usual operations of addition and multiplacation on R^2×2
Explanation / Answer
+ The set R of real numbers under the usual operations of addition and multiplacation.
Yes, it is a vector space.
+ The set {(x,0)¦x € R} under the usual operations of addition and multiplacation on R^2
Yes, it is a vector space.
+ The set {(x,1)¦x € R} under the usual operations of addition and multiplacation on R^2
No, it is not a vector space. Zero vector is not in the set.
+The set {(x,0) ¦x € R, x=0} under the usual operations of addition and multiplacation on R^2
Yes, it is a vector space.
+The set {(x,1) ¦x € R, x=0} under the usual operations of addition and multiplacation on R^2
No, it is not a vector space. Zero vector is not in the set.
+The set { [ a a+b] }
{ [ a+b a ] ¦a,b € R } under the usual operations of addition and multiplacation on R^2×2
Yes, it is a vector space.
+The set { [a a+b+1] }
{ [a+b a ] ¦a,b € R} under the usual operations of addition and multiplacation on R^2×2
Not a vector space. Zero vector is not in the set.
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