# Matrices, Vector Spaces and Zero Vector

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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?

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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.

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