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Properties of Vector Multiplication by Scalar

Properties of Vector Multiplication by Scalar

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Applicable Properties for Vector Multiplication by Scalar


 »  Applicable properties for Addition and Multiplication
These are named only for Addition and Multiplication
    →  closure
    →  commutative
    →  associative
    →  distributive
    →  identity
    →  inverse


 »  Multiplication of Vector by Scalar is multiplication of real numbers
    →  individual components on `3` axes are real numbers
    →  the components are multiplied independently
    →  properties of "multiplication of vector by scalar" is equivalently that of real-number addition

Applicable Properties and understanding them

plain and simple summary

nub

plain and simple summary

nub

dummy

Multiplication of vector by a scalar is defined between two different entities - a scalar and a vector. The applicable properties are given in the coming pages.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn about the applicable properties of multiplication of vector by scalar.


Keep tapping on the content to continue learning.
Starting on learning "understanding the applicable properties of multiplication of vector by scalar". ;;

For an arithmetic operation, usually, we learn the following properties

 • closure,

 • commutative,

 • associative,

 • distributive,

 • Identity with respect to the operation

 • Inverse with respect to the operation These properties are studied for addition and multiplication only.

When studying these properties, subtraction is considered to be inverse of addition, and division is considered to be inverse of multiplication.

If commutative property is to be applied for `a-b`, it has to be `a + (-b)` and commutative property of addition is applied.

If commutative property is to be applied for `a-:b`, it has to be `a xx (1/b)` and commutative property of multiplication is applied

If associative property is to be applied for `(a-b)-c`, it has to be `[a+(-b)]+ (-c)` and associative property of addition is applied.

If associative property is to be applied for `(a-:b)-:c`, it has to be `[a xx (1/b)] xx (1/c)` and associative property of multiplication is applied.

Apart from the 4 fundamental operations, for other arithmetic operations like modulus, these properties are not called using the standard names like closure property.

For example, take modulus of a number. Even though, it is established that modulus of a real number is a real number, it is not referred as closure property of modulus. The properties are exclusively studied for addition and multiplication.

The set of properties are studied for Addition and Multiplication.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy


           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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For an arithmetic operation, usually, we learn the following properties ;;closure, ;;commutative, ;;associative, ;;distributive, ;;Identity with respect to the operation ;;Inverse with respect to the operation These properties are studied for addition and multiplication only.
When studying these properties, subtraction is considered to be inverse of addition, and division is considered to be inverse of multiplication.
If commutative property is to be applied for a minus b, it has to be a plus minus b and commutative property of addition is applied. ;; If commutative property is to be applied for a divided by b, it has to be a multiplied 1 by b and commutative property of multiplication is applied.
If associative property is to be applied for a minus b minus c, it has to be a plus minus b plus minus c and associative property of addition is applied. ;; If associative property is to be applied for a divided by b divided by c , it has to be a multiplied 1 by b multiplied by 1 by c and associative property of multiplication is applied.
Apart from the 4 fundamental operations, for other arithmetic operations like modulus, these properties are not called using the standard names like closure property. ;; For example, take modulus of a number. Even though, it is established that modulus of a real number is a real number, it is not referred as closure property of modulus. The properties are exclusively studied for addition and multiplication.
The set of properties are studied for Addition and Multiplication.
Multiplication of vector by a scalar is defined between two different entities - a scalar and a vector. The applicable properties are given in the coming pages.

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