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Properties of Matrix Addition Video Lecture | Mathematics (Maths) Class 12 - JEE

Q: 1. What are the properties of matrix addition?

Ans. Matrix addition has the following properties:- Commutative property: The order of matrix addition does not matter. A + B = B + A.- Associative property: Matrix addition is associative, meaning that (A + B) + C = A + (B + C).- Identity property: There exists an identity matrix, denoted by 0, such that A + 0 = A for any matrix A.- Inverse property: For every matrix A, there exists a matrix -A such that A + (-A) = 0.- Closure property: The sum of two matrices is always a matrix.

	Mathematics (Maths) Class 12 204 videos\|290 docs\|139 tests

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204 videos|290 docs|139 tests

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FAQs on Properties of Matrix Addition Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What are the properties of matrix addition?

Ans. Matrix addition has the following properties: - Commutative property: The order of matrix addition does not matter. A + B = B + A. - Associative property: Matrix addition is associative, meaning that (A + B) + C = A + (B + C). - Identity property: There exists an identity matrix, denoted by 0, such that A + 0 = A for any matrix A. - Inverse property: For every matrix A, there exists a matrix -A such that A + (-A) = 0. - Closure property: The sum of two matrices is always a matrix.

2. Can we add matrices of different sizes?

Ans. No, matrices of different sizes cannot be added together. In order to perform matrix addition, the matrices must have the same dimensions. The number of rows and columns in both matrices must be equal.

3. What is the result of adding two matrices with different dimensions?

Ans. If two matrices have different dimensions, matrix addition is not possible. The operation is undefined and cannot be performed. It is important to ensure that the matrices being added have the same number of rows and columns.

4. How do we perform matrix addition?

Ans. To add two matrices, simply add the corresponding elements in the matrices. For example, if we have matrices A and B, with A = [a11 a12; a21 a22] and B = [b11 b12; b21 b22], the sum A + B will be [a11 + b11 a12 + b12; a21 + b21 a22 + b22].

5. Can matrix addition be used to solve systems of linear equations?

Ans. Matrix addition alone cannot be used to solve systems of linear equations. However, it is a useful tool in matrix operations and can be used in conjunction with other operations, such as matrix multiplication and inverse, to solve systems of linear equations.

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	Nov 22, 2024 Last updated

Video Description: Properties of Matrix Addition for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The notes and questions for Properties of Matrix Addition have been prepared according to the JEE exam syllabus. Information about Properties of Matrix Addition covers all important topics for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Properties of Matrix Addition.

Introduction of Properties of Matrix Addition in English is available as part of our Mathematics (Maths) Class 12 for JEE & Properties of Matrix Addition in Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free.

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