Скачать или смотреть Matrix Long Question Optional Maths | Prove Given Equations | Class 10 Optional Mathematics Nepal

Welcome to Everest Online Academy! In this video, we explore how to solve long matrix questions , specifically when you are given a matrix A and asked to verify that it satisfies a given condition , a key topic in the Class 10 Optional Mathematics syllabus under the chapter Matrices . Understanding how to manipulate matrices and verify conditions is crucial for scoring well in your SEE exams. Whether you're struggling with matrix operations or need help solving numerical problems step-by-step, this video will guide you with clear explanations and solved examples.

✅ What You’ll Learn in This Video:

Introduction to Matrices :
What are Matrices? (Definition and Importance)
Types of Matrices:
Square Matrix.
Identity Matrix.
Zero Matrix.
Operations on Matrices:
Addition, Subtraction, and Multiplication.
Transpose of a Matrix.
Determinant of a Matrix.
Key Concepts :
Verifying Conditions for a Given Matrix :
Example Problem:
Given a matrix A=[
2
1
​

3
4
​
], verify that A
2
−5A+6I=0, where I is the identity matrix.
Solution:
Step 1: Compute A
2
:
A
2
=A⋅A=[
2
1
​

3
4
​
]⋅[
2
1
​

3
4
​
]
A
2
=[
7
6
​

18
19
​
]
Step 2: Compute 5A:
5A=5⋅[
2
1
​

3
4
​
]=[
10
5
​

15
20
​
]
Step 3: Compute 6I:
6I=6⋅[
1
0
​

0
1
​
]=[
6
0
​

0
6
​
]
Step 4: Substitute into the equation A
2
−5A+6I:
A
2
−5A+6I=[
7
6
​

18
19
​
]−[
10
5
​

15
20
​
]+[
6
0
​

0
6
​
]
A
2
−5A+6I=[
3
1
​

3
5
​
]−[
3
1
​

3
5
​
]=[
0
0
​

0
0
​
]
Thus, A
2
−5A+6I=0 is verified.
Step-by-Step Solutions to SEE Past Year Questions :
Solving numerical problems involving verifying conditions for matrices.
Application of concepts in real exam questions.
Common Mistakes to Avoid While Solving Matrix Problems
Tips to Score Full Marks in Optional Mathematics Questions
Practice Exercises for Better Understanding
💡 Why Watch This Video?
The Matrix Long Questions chapter is a frequently tested topic in the Class 10 Optional Mathematics exam, especially in the context of verifying conditions for matrices. By mastering these calculations, you can confidently tackle exam questions and secure full marks in this section. This video simplifies the theory, provides solved examples, and includes practical tips to ensure you’re fully prepared.

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💬 Let’s Discuss:
Have any doubts or questions about Matrix Long Questions or related topics? Drop them in the comments below, and we’ll get back to you as soon as possible. Also, let us know what other topics or SEE questions you’d like us to cover in future videos.

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