Multiplication of a Matrix by a Number

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 = [10537] and B = [290315]

Then, kA = k[10537]

              = [10k5k3k7k] and

kB = k[290315]

     = [2k9k03k1k5k]


Similarly,

[abcd] = 1k[kakbkckd].

Multiplication of a Matrix by a Scalar

Solved examples on Multiplication of a Matrix by a Number (Scalar Multiplication):

1. If A = [10914], find 4A.

Solution:

4A = 4[10914]

     = [4×104×(9)4×(1)4×4]

     = [4036416]

Scalar Multiplication of Matrix

 

2. If M = [2345], find -5A.

Solution:

-5M = -5[2345]

       = [(5)×2(5)×(3)(5)×(4)(5)×5]

       = [10152025]





10th Grade Math

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