Share
Explore BrainMass

Matrices, Vector Spaces and Zero Vector

a 1
Show(prove) that the set of all 2 X 2 matrices of the form with addition defined by
1 b

a 1 c 1 a+c 1
+ =
1 b 1 d 1 b+d

a 1 ka 1
and scalar multiplication defined by: k * =
1 b 1 kb

is a vector space . What is the zero-vector in this space?

Attachments

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

a 1
Show(prove) that the set of all 2 X 2 matrices of the form with addition defined by
1 b

a 1 c 1 a+c 1
+ =
...

Solution Summary

Matrices, Vector Spaces and Zero Vectors are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19