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I'm have problem proving: Law for Scalar Multiplication :

Vector spaces possess a collection of specific characteristics and properties. Use the definitions in the attached “Definitions” to complete this task.

Define the elements belonging to $\mathbb{R}^2$ as $\{(a, b) | a, b \in \mathbb{ R}\}$. Combining elements within this set under the operations of vector addition and scalar multiplication should use the following notation:

Vector Addition Example: $(–2, 10) + (–5, 0) = (–2 – 5, 10 + 0) = (–7, 10)$

Scalar Multiplication Example: $–10 × (1, –7) = (–10 × 1, –10 × –7) = (–10, 70)$, where –10 is a scalar.

Under these definitions for the operations, it can be rigorously proven that R2 is a vector space.

Prove Closure under Scalar Multiplication - **i need help with this law **

I'm have problem proving: Law for Scalar Multiplication :

Vector spaces possess a collection of specific characteristics and properties. Use the definitions in the attached “Definitions” to complete this task.

Define the elements belonging to $\mathbb{R}^2$ as $\{(a, b) | a, b \in \mathbb{ R}\}$. Combining elements within this set under the operations of vector addition and scalar multiplication should use the following notation:

Vector Addition Example: $(–2, 10) + (–5, 0) = (–2 – 5, 10 + 0) = (–7, 10)$

Scalar Multiplication Example: $–10 × (1, –7) = (–10 × 1, –10 × –7) = (–10, 70)$, where –10 is a scalar.

Under these definitions for the operations, it can be rigorously proven that R2 is a vector space.

Prove Closure under Scalar Multiplication - **i need help with this law **

Can someone put it in a proof form?

I'm have problem proving: Law for Scalar Multiplication :

Vector spaces possess a collection of specific characteristics and properties. Use the definitions in the attached “Definitions” to complete this task.

Define the elements belonging to $\mathscr R^2$ as $\{(a, b) | a, b \in \mathscr R\}$. Combining elements within this set under the operations of vector addition and scalar multiplication should use the following notation:

Vector Addition Example: $(–2, 10) + (–5, 0) = (–2 – 5, 10 + 0) = (–7, 10)$

Scalar Multiplication Example: $–10 × (1, –7) = (–10 × 1, –10 × –7) = (–10, 70)$, where –10 is a scalar.

Under these definitions for the operations, it can be rigorously proven that R2 is a vector space.

Prove Closure under Scalar Multiplication - **i need help with this law **

I'm have problem proving: Law for Scalar Multiplication :

Vector spaces possess a collection of specific characteristics and properties. Use the definitions in the attached “Definitions” to complete this task.

Define the elements belonging to $\mathbb{R}^2$ as $\{(a, b) | a, b \in \mathbb{ R}\}$. Combining elements within this set under the operations of vector addition and scalar multiplication should use the following notation:

Vector Addition Example: $(–2, 10) + (–5, 0) = (–2 – 5, 10 + 0) = (–7, 10)$

Scalar Multiplication Example: $–10 × (1, –7) = (–10 × 1, –10 × –7) = (–10, 70)$, where –10 is a scalar.

Under these definitions for the operations, it can be rigorously proven that R2 is a vector space.

Prove Closure under Scalar Multiplication - **i need help with this law **

I'm have problem proving: Law for Scalar Multiplication :

Vector spaces possess a collection of specific characteristics and properties. Use the definitions in the attached “Definitions” to complete this task.

Define the elements belonging to R2 as {(a, b) | a, b ∈ R}. Combining elements within this set under the operations of vector addition and scalar multiplication should use the following notation:

Vector Addition Example: (–2, 10) + (–5, 0) = (–2 – 5, 10 + 0) = (–7, 10)

Scalar Multiplication Example: –10 × (1, –7) = (–10 × 1, –10 × –7) = (–10, 70), where –10 is a scalar.

Under these definitions for the operations, it can be rigorously proven that R2 is a vector space.

Prove Closure under Scalar Multiplication - **i need help with this law **

I'm have problem proving: Law for Scalar Multiplication :

Vector spaces possess a collection of specific characteristics and properties. Use the definitions in the attached “Definitions” to complete this task.

Define the elements belonging to $\mathscr R^2$ as $\{(a, b) | a, b \in \mathscr R\}$. Combining elements within this set under the operations of vector addition and scalar multiplication should use the following notation:

Vector Addition Example: $(–2, 10) + (–5, 0) = (–2 – 5, 10 + 0) = (–7, 10)$

Scalar Multiplication Example: $–10 × (1, –7) = (–10 × 1, –10 × –7) = (–10, 70)$, where –10 is a scalar.

Under these definitions for the operations, it can be rigorously proven that R2 is a vector space.

Prove Closure under Scalar Multiplication - **i need help with this law **