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Dipendu Maity replied | 6 days ago

A vector space is a set of vectors that are closed under vector addition and scalar multiplication, meaning adding two vectors or multiplying a vector by a scalar results in another vector within the same set. These operations must satisfy a specific set of rules, or axioms, ensuring the structure is well-defined and can be used for things like linear algebra. Common examples include the set of all possible dimensional real number pairs and the set of polynomials.

Prashant Nirala replied | 5 days ago

A vector space is a mathematical structure formed by a collection of vectors, which can be added together and multiplied (“scaled”) by numbers, called scalars. Scalars are often taken to be real numbers. The operations of vector addition and scalar multiplication must satisfy nine rules such as associativity, commutativity, existence of a zero vector, and distributivity. Vector spaces are foundational in linear algebra.

Sana Begum replied | 27 Oct

create a structured routine by setting specific study times, organizing your workspace, and using a calendar to manage deadlines.

Sonia replied | 01 Nov

balance your schedule by using a calendar and planner, communicate with your employer and support network, and create a dedicated study space free from distractions. Stay organized by breaking down tasks, setting clear goals, and leveraging online resources and tools.

Saurabh Verma replied | 24 Oct

Articulation in music means how you play each note — whether it’s smooth, short, or strong.

Here are some simple examples:

Staccato (•) → Play the note short and jumpy.

Legato (curved line) → Play smoothly, join one note to the next.

Accent ( > ) → Play the note louder or stronger.

Tenuto (–) → Hold the note for its full time, a bit gentle.

Marcato ( ^ ) → Play the note very strong and bold.

🎹 In short way:

Articulation shows how to touch or press the keys — softly, sharply, or smoothly — to make the music sound more expressive.

Saurabh Verma replied | 24 Oct

Articulation in music means how you play each note — whether it’s smooth, short, or strong.

Here are some simple examples:

Staccato (•) → Play the note short and jumpy.

Legato (curved line) → Play smoothly, join one note to the next.

Accent ( > ) → Play the note louder or stronger.

Tenuto (–) → Hold the note for its full time, a bit gentle.

Marcato ( ^ ) → Play the note very strong and bold.

🎹 In short way:
Articulation shows how to touch or press the keys — softly, sharply, or smoothly — to make the music sound more expressive.