Matrices: Operations and Equality Explained

In the realm of matrices, equality is determined by matching corresponding elements, while addition and subtraction follow specific rules. Understanding the properties of equality, commutative and associative laws, as well as the impact of matrix size on addition and subtraction, is essential for mastering matrix operations.

• Matrices
• Operations
• Equality
• Laws
• Addition

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Uploaded on Apr 21, 2025 | 0 Views

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Presentation Transcript

1. Matrices Matrix Operations

2. Matrices - Operations EQUALITY OF MATRICES Two matrices are said to be equal only when all corresponding elements are equal Therefore their size or dimensions are equal as well 1 0 0 1 0 0 A = A = B B = 2 1 0 2 1 0 5 2 3 5 2 3

3. Matrices - Operations Some properties of equality: IIf A = B, then B = A for all A and B IIf A = B, and B = C, then A = C for all A, B and C 1 0 0 b b b 11 12 13 A = B = 2 1 0 b b b 21 22 23 5 2 3 b b b 31 32 33 a = b If A = B then ij ij

4. Matrices - Operations ADDITION AND SUBTRACTION OF MATRICES The sum or difference of two matrices, A and B of the same size yields a matrix C of the same size = + c a b ij ij ij Matrices of different sizes cannot be added or subtracted

5. Matrices - Operations Commutative Law: A + B = B + A Associative Law: A + (B + C) = (A + B) + C = A + B + C 6 7 3 1 1 5 6 8 8 5 + = 2 5 4 2 3 2 7 9 B C A 2x3 2x3 2x3

6. Matrices - Operations A + 0 = 0 + A = A A + (-A) = 0 (where A is the matrix composed of aij as elements) 6 4 2 1 2 0 5 2 2 = 3 2 7 1 0 8 2 2 1