Label the following statements true are false and justifyyour answer please.
a} Every vector space contains a zero vector.
b} A vector space may have more than one zero vector.
Solution
1. TRUE. In a vector space, there is closure ofaddition and scalar multiplication.
Let v be in VS. Then (-1)v = -v is in VS. So v +-v = 0 is in VS.
.
2. FALSE. Let 01 and 02 bezero vectors. Then v1+01=v1 andv2+02=v2 for all vectorsvi in the
VS. Let v1=02and v2=01. So, we have02+01=02 and01+02=01. This implies01=02, so the zero
vector isunique..
Label the following statements true are false and justifyyour answer.pdf
1. Label the following statements true are false and justifyyour answer please.
a} Every vector space contains a zero vector.
b} A vector space may have more than one zero vector.
Solution
1. TRUE. In a vector space, there is closure ofaddition and scalar multiplication.
Let v be in VS. Then (-1)v = -v is in VS. So v +-v = 0 is in VS.
.
2. FALSE. Let 01 and 02 bezero vectors. Then v1+01=v1 andv2+02=v2 for all vectorsvi in the
VS. Let v1=02and v2=01. So, we have02+01=02 and01+02=01. This implies01=02, so the zero
vector isunique.
