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

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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.
204 videos|288 docs|139 tests

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