Kharagpur

Ayush replied | 22 hrs ago

A vector space is a collection of things called vectors that you can add together and multiply by numbers (called scalars), and the results still belong to the same collection.

🧠 Example:

Think of arrows on a page — each arrow has a direction and a length.

• If you add two arrows (by joining them tip-to-tail), you get another arrow.

• If you stretch or shrink an arrow (multiply by a number), you still get another arrow.

All such arrows together form a vector space.

Anubhav Mourya replied | 14 hrs ago

A vector space is a fundamental concept in mathematics, particularly in linear algebra. It is a set of elements called vectors, along with two operations: vector addition and scalar multiplication. These operations allow you to add two vectors together and multiply a vector by a scalar (a number from a field, usually real or complex numbers) in such a way that certain rules, called axioms, are always satisfied

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 | 5 days ago

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.