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Thought-Process to Discover Knowledge

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### Closure Property of Vector Addition

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What does 'closure' mean?

• closed
• not open
• both the above
• both the above

Integer addition has closure property. It means that, if any two integers are added, the result will be within the integer set of numbers. Is it correct?

• Yes, the result has to be within
• Yes, the result has to be within
• No, the result has to be outside

Answer is 'Result has to be within' the set of integers.

Vector space bbb V consists of all the vectors with real numbers as components.

Is sum of two vectors be another vector in the vector space?

• Yes
• Yes
• No

The answer is 'Yes'. Sum of two real-numbers is a real number. Since vector addition is addition of real-numbers as components, sum of vectors is a vector.

•  Sum or difference of two vectors is another vector - closed.

Closure Property of Vector Addition: For any vectors  vec(a), vec(b) in bbb V,
 vec(a)+vec(b) in bbb V

slide-show version coming soon