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# Operations on Matrices - Properties of Scalar Multiplication of a Matrix

#### notes

If A = [a_(ij)] and B = [b_(ij)] be two matrices of the same order, say m × n, and k and l are scalars, then
(i) k(A +B) = k A + kB,

(ii) (k + l)A = k A + l A

(iii) k (A + B) = k ([a_(ij)] + [b_(ij)])

= k [a_(ij) + b_(ij)] = [k (a_(ij) + b_(ij))] = [(k a_(ij)) + (k b_(ij))]
= [k a_(ij)] + [k b_(ij)] = k [a_(ij)] + k [b_(ij)] = kA + kB

(iv) (k + l) A = (k + l) [a_(ij)]
= [(k + l) a_(ij)] + [k a_(ij)] + [l a_(ij)]
= k [a_(ij)] + l [a_(ij)]
= k A + l A

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