Several operations such as arithmetic operations can be performed on matrices.
- [tex]\mathbf{BD = 2 \times 1}[/tex].
- [tex]\mathbf{CA = 1 \times 2}[/tex].
- [tex]\mathbf{DC = 2 \times 3}[/tex]
The product of a matrix is represented as:
[tex]\mathbf{(m \times n) \cdot (n \times k) = (m \times k)}[/tex]
The dimension of the matrices are given as:
- [tex]\mathbf{A = 3 \times 2}[/tex].
- [tex]\mathbf{B = 2 \times 2}[/tex].
- [tex]\mathbf{C = 1 \times 3}[/tex].
- [tex]\mathbf{D = 2 \times 1}[/tex].
(a) Product BD
We have:
[tex]\mathbf{B = 2 \times 2}[/tex]
[tex]\mathbf{D = 2 \times 1}[/tex]
So, the product of BD is:
[tex]\mathbf{BD = B \times D}[/tex]
This gives
[tex]\mathbf{BD = (2 \times 2) \cdot (2 \times 1)}[/tex]
Using: [tex]\mathbf{(m \times n) \cdot (n \times k) = (m \times k)}[/tex]
We have:
[tex]\mathbf{BD = 2 \times 1}[/tex]
(b) Product CA
We have:
[tex]\mathbf{A = 3 \times 2}[/tex]
[tex]\mathbf{C = 1 \times 3}[/tex]
So, the product of CA is:
[tex]\mathbf{CA= C \times A}[/tex]
This gives
[tex]\mathbf{CA = (1 \times 3) \cdot (3 \times 2)}[/tex]
Using: [tex]\mathbf{(m \times n) \cdot (n \times k) = (m \times k)}[/tex]
We have:
[tex]\mathbf{CA = 1 \times 2}[/tex]
(c) Product DC
We have:
[tex]\mathbf{C = 1 \times 3}[/tex]
[tex]\mathbf{D = 2 \times 1}[/tex]
So, the product of DC is:
[tex]\mathbf{DC= D \times C}[/tex]
This gives
[tex]\mathbf{DC = (2 \times 1) \cdot (1 \times 3)}[/tex]
Using: [tex]\mathbf{(m \times n) \cdot (n \times k) = (m \times k)}[/tex]
We have:
[tex]\mathbf{DC = 2 \times 3}[/tex]
Read more about product of matrices at:
https://brainly.com/question/24810141
