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4.4 Matrices: Basic Operations •Addition and subtraction of matrices •Product of a number k and a matrix M •Matrix Product. Addition and Subtraction of matrices To add or subtract matrices, they must be of the same size mxn. To add matrices of the same size, add their corresponding entries. ! $ ! $ 1 2 4 5 A+B=!a +b # # & +# & = " % " % " ij ij $ 5 2 9 1 To subtract matrices of the same order, subtract their corresponding entries. The general rule is as follows using mathematical notation: ! $ ! $ A!B="a !b $ 1 2 ' 4 5 = ij ij # & # & " % " % # % 5 2 9 1 More examples: "4 !3 1 % "!1 2 3% $0 5 !2'+$6 !7 9' $ ' $ ' $5 !6 0 ' $ 0 !4 8' # & # & "4 !3 1 % "!1 2 3% $0 5 !2'!$6 !7 9' $ ' $ ' $5 !6 0 ' $ 0 !4 8' # & # & "4 !3 1 % "1 5% $0 5 !2'!$3 7' $ ' $ ' $5 !6 0 ' $1 2' # & # & ! # ! # 1 6 3 % %2 3 1 " $ " $ Scalar Multiplication The scalar product of a number k and a matrix A is the matrix denoted by kA, obtained by multiplying each entry of A by the number k . The number k is called a scalar. kA=!ka " # ij $ Example: "!1 2 3% (!1)$ 6 !7 9' $ ' $ 0 !4 8' # &
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