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Unformatted text preview: », Âµ âˆˆ R.
1 A + B = B + A (addition is commutative). 2 (A + B ) + C = A + (B + C ) (addition is associative). 3 (Î»Âµ)A = Î»(ÂµA) (scalar multiplication is associative). 4 (Î» + Âµ)A = Î»A + ÂµA (matrices distribute through scalar
multiplication). 5 Î»(A + B ) = Î»A + Î»B (scalar multiplication distributes
through matrix addition). Outline Matrices Matrix Algebra Matrix Equations Trace and Transpose Properties of Addition and Scalar Multiplication Theorem
The following equations hold for any m Ã— n matrices A, B, and C ,
and scalars Î», Âµ âˆˆ R.
1 A + 0 = A = 0 + A where 0 is the n Ã— m zero matrix (0 is the
additive identity). 2 A âˆ’ A = 0 (A and âˆ’A are additive inverses). 3 0A = 0 = A0 where 0A represents scalar multiplication and 0
represents the n Ã— m zero matrix. Proof.
Use properties of real numbers applied entry by entry. Outline Matrices Matrix Algebra Matrix Equations Trace and Transpose The Product of a Matrix and a Column Vector
Let A = (aij ) be an m Ã— n matrix hav...
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This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.
 Spring '14
 KenyonJ.Platt
 Linear Algebra, Algebra, Equations, Matrices

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