Chapter 1.2 MatrixAlgebra

# 1 2 3 4 1 3 4 2 123 a 1 1 0 1 c 0 1 2 0 2 3 4 000 b a

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Unformatted text preview: 2 123 A= 1 −1 0 1 C = 0 1 2 0 2 3 4 000 B= a= 000 000 2 −3 0 1 1 0 D= 0 0 0 0 0 0 0 0 0 0 5 0 0 −2 b= 5 −4 −3 0 9 Outline Matrices Matrix Algebra Matrix Equations Trace and Transpose Matrix Operations Deﬁnition Let A = [aij ] and B = [bij ] be two m × n matrices, and let λ be a scalar. 1 The sum of A and B is the m × n matrix A + B deﬁned by: A + B = [aij ] + [bij ] = [aij + bij ]. 2 The diﬀerence of A and B is the m × n matrix A − B deﬁned by: A − B = [aij ] − [bij ] = [aij − bij ]. 3 The scalar multiple of A by λ is the m × n matrix λA deﬁned by: λA = λ[aij ] = [λaij ]. Outline Matrices Matrix Algebra Matrix Equations Examples Example Find A + B , A − B , and −2A, where A= 2 −4 1 6 5 −10 and B = −9 73 1 −3 8 Trace and Transpose Outline Matrices Matrix Algebra Matrix Equations Trace and Transpose Properties of Addition and Scalar Multiplication Theorem The following equations hold for any m × n matrices A, B, and C , and scalars...
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