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We will discuss here about the process of Multiplication of a matrix by a number.
The multiplication of a matrix A by a number k gives a matrix of the same order as A, in which all the elements are k times the elements of A.
Example:
Let A = [105β3β7] and B = [β2903β15]
Then, kA = k[105β3β7]
= [10k5kβ3kβ7k] and
kB = k[β2903β15]
= [β2k9k03kβ1k5k]
Similarly,
[abcd] = 1k[kakbkckd].
Solved examples on Multiplication of a Matrix by a Number
(Scalar Multiplication):
1. If A = [10β9β14], find 4A.
Solution:
4A = 4[10β9β14]
= [4Γ104Γ(β9)4Γ(β1)4Γ4]
= [40β36β416]
2. If M = [2β3β45], find -5A.
Solution:
-5M = -5[2β3β45]
= [(β5)Γ2(β5)Γ(β3)(β5)Γ(β4)(β5)Γ5]
= [β101520β25]
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