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Matrix add
Matrix Addition Matrix addition is a mathematical operation that combines two matrices to form a third matrix. Each element in the resulting matrix is calcul...
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Matrix Addition Matrix addition is a mathematical operation that combines two matrices to form a third matrix. Each element in the resulting matrix is calcul...
Matrix addition is a mathematical operation that combines two matrices to form a third matrix. Each element in the resulting matrix is calculated by adding the corresponding elements in the corresponding positions of the original matrices.
Here's how it works:
Matrix dimensions:
Matrix A must have the same number of rows as matrix B.
Matrix A must have the same number of columns as matrix C.
Matrix B must have the same number of rows as matrix C.
Adding the elements:
For each element in the resulting matrix, add the corresponding elements in the matrices A and B.
The order of the elements is preserved: first row of A, then column 1 of A, then row 1 of B, and so on.
Example:
Let's say we have the following two matrices:
A = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
B = [
[10, 11, 12],
[13, 14, 15],
[16, 17, 18]
]
Adding the matrices A and B, we get the following result:
A + B = [
[1, 3, 9],
[18, 21, 27],
[25, 27, 36]
]
Key points about matrix addition:
It is a linear operation, meaning the resulting matrix is also a matrix.
It is commutative, meaning A + B = B + A.
It is not a linear operation when the matrices have different dimensions