Symmetric and Skew Symmetric Matrix for NDA | Complete Concept | By Dheeraj sir | MISSION SELECTION

Symmetric and Skew Symmetric Matrix for NDA | Complete Concept | By Dheeraj sir | MISSION SELECTION
This video by Dheeraj sir from MISSION SELECTION provides a comprehensive explanation of Symmetric and Skew-Symmetric Matrices, crucial for NDA and other competitive exams (0:00).

The video covers:

Definitions:
Symmetric Matrix: A matrix 'A' is symmetric if its transpose (Aᵀ) is equal to itself (Aᵀ = A) (2:17).
Skew-Symmetric Matrix: A matrix 'A' is skew-symmetric if its transpose (Aᵀ) is equal to the negative of itself (Aᵀ = -A) (2:40).
Key Characteristics and Properties:
Symmetric Matrix (3:55):
Recognized by a "mirror image" pattern around the diagonal elements (7:00).
The element at position aij is equal to the element at aji (9:49).
If 'A' is a symmetric matrix, then A raised to any power 'n' (Aⁿ) is also a symmetric matrix (11:01).
Skew-Symmetric Matrix (12:35):
All diagonal elements are always zero (16:50).
The trace (sum of all diagonal elements) of a skew-symmetric matrix is always zero (18:00).
The element at position aij is equal to the negative of the element at aji (aij = -aji) when i ≠ j (21:00). When i = j (diagonal elements), aij = 0 (21:31).
The sum of all elements in a skew-symmetric matrix is always zero (23:30).
Determinant Properties:
If the order of the matrix is odd, its determinant is always zero (e.g., 3x3, 5x5) (27:30).
If the order of the matrix is even, its determinant is always a perfect square number (e.g., 2x2, 4x4) (28:15).
Power of Skew-Symmetric Matrix:
If 'n' is odd, Aⁿ is a skew-symmetric matrix (31:04).
If 'n' is even, Aⁿ is a symmetric matrix (31:45).
The video also includes solved examples and discusses common NDA exam questions related to these matrix types and their properties (33:37). Notably, it explains properties related to the sum and difference of a matrix and its transpose (A + Aᵀ is symmetric, A - Aᵀ is skew-symmetric) (35:21).
इस वीडियो में हम Symmetric और Skew Symmetric Matrix को बिल्कुल आसान भाषा में समझेंगे। यह टॉपिक Matrix Chapter का एक बहुत ही महत्वपूर्ण हिस्सा है और NDA में बार-बार पूछा जाता है।
वीडियो में आप सीखेंगे –
✔ Symmetric Matrix की परिभाषा
✔ Skew Symmetric Matrix की परिभाषा
✔ दोनों के बीच अंतर (Difference)
✔ Important Properties
✔ Solved Examples
✔ Exam में पूछे जाने वाले प्रश्न
अगर आप Matrix को strong बनाना चाहते हैं और NDA Maths में अच्छे अंक लाना चाहते हैं, तो यह वीडियो आपके लिए बहुत उपयोगी है। Concept को step-by-step समझाया गया है ताकि हर student आसानी से समझ सके।
📌 यह वीडियो Mission Selection चैनल द्वारा सभी Competitive Exams के छात्रों के लिए बनाया गया है।
वीडियो पसंद आए तो Like, Share और Subscribe ज़रूर करें।

#SymmetricMatrix
#SkewSymmetricMatrix
#MatrixChapter
#Matrices
#NDAMaths
#NDAExam
#AllCompetitiveExams
#MathsForNDA
#MatrixImportantQuestions
#ExamOrientedMaths
#MissionSelection
#MathsConcept
#Class12Maths
#CompetitiveMaths