Matrix Operations: Addition, Subtraction, and Scalar Multiplication

Jan 14, 2026

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In matrix algebra, the sum of two m×n matrices A and B, denoted A + B, is obtained by adding their corresponding entries. Conversely, the difference A - B is found by subtracting corresponding entries of A and B. Additionally, for an m×n matrix A and a scalar s, the matrix kA is produced through scalar multiplication, which involves multiplying every entry of A by k. It is worth noting that the product of matrices AB does not equal BA, demonstrating the non-commutative nature of matrix multiplication.

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Matrix Operations: Addition, Subtraction, and Scalar Multiplication

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Section 7.4 Matrix Algebra

If A and B are both m×n matrices then the sum of A and B, denoted A + B, is a matrix obtained by adding correspondingentries of A and B. The difference of A and B, denoted A - B, is obtained by subtracting correspondingentries of A and B.

The Zero Matrix

If A is an m×n matrix and s is a scalar, then we let kA denote the matrix obtained by multiplying every element of A by k. This procedure is called scalar multiplication.