Calculate using Matrices.

 This is how you calculate, but with rows and columns. 

• What is Matrix
• Matrices Addition
• Matrices Subtraction
• Matrix multiplication by scalar
• Matrices Multiplication

What is Matrix

Matrix is a condition where numbers are arranged to rows and columns.

(rows x columns).

Let's call matrix A:

As we can see, the matrix A has numbers such as 6, 3, -4 and 10. The columns of matrix A are two, the first column has number 6 and -4. While the second column has number 3 and 10. How about the rows? The first row has number 6 and 3, while second row has number -4 and 10. 

How to determine matrix element? Below is how.

Continue on looking on matrix A above, let's say that Ali want to know what is a₁,₁. The first 1 subscript means the number at the first row, the second 1 subscript means the number at first column. So, a₁,₁ is 6. Below is the answer for each matrix A element:

a₁,₁=6

a₁,₂=3

a₂,₁=-4

a₂,₂=10

For more information, look here to know matrix introduction.

Matrices Addition

The addition between two matrices is processed according to the elements' position of two matrices. See the example in the picture below:

The picture above shows the addition of two matrices, B and C. Both of the matrices are 3x2, means 3 rows and 2 columns. The B matrix has elements such as 3, 3, 5, 12, 7 and 6, while C matrix has elements (numbers) like 5, 0, 5, 8, 6 and 1. Then, the addition process taking place, where the elements are added according to their positions. For example, b₃,₁ (7) perform addition with c₃,₁ (6). Then, solve the addition as the picture above. 

Matrices Subtraction

The subtraction process for matrices is the similar process with addition for matrices in terms of elements' position. The difference are the operation involved. See the example of matrices subtraction below:

Above is the subtraction between matrix D and matrix E. Below is the result of subtractions based on matrices' elements:

d₁,₁- e₁,₁= 1-7=-6

d₁,₂- e₁,₂= 2-8=-6

d₁,₃- e₁,₃= 3-9=-6

d₂,₁- e₂,₁= 4-10=-6

d₂,₂- e₂,₂= 5-11=-6

d₂,₃- e₂,₃= 6-12=-6 #

Look here to find out addition and subtraction of matrices.

Matrix multiplication by scalar

This process is also called "multiplicative identity property". The usage of this multiplication by scalar can be applicate to estimate the 300 persons on value of average income per month, average number of children and average value of houses. By the another example below, we should understand the application further:

The above picture shows the scalar multiplication of matrix between 5 and F. The number 5 is expanded to each of F elements to multiply to each of them. Below are the multiply results of 5 and F elements:

5 ⸳ f₁,₁ = 5 ⸳ 3 = 15

5 ⸳ f₁,₂ = 5 ⸳ 6 = 30

5 ⸳ f₂,₁ = 5 ⸳ 9 = 45

5 ⸳ f₂,₂ = 5 ⸳ 11 = 55 #

Matrices Multiplication

The matrices multiplication is the process when two matrices are multiplying each other. Remember that rows from first matrix are multiplying with columns from second matrix. The example is shown below:

Based on the picture above, the matrix G is multiplied by H. The upper left corner of the answer (20) is result of multiplication of G's first row and H's first column. 28 is result of multiplication of G's first row and H's second column. 46 is result of multiplication of G's second row and H's first column. Then, 76 is result of multiplication of G's second row and H's second column. 

Note that the dot in picture above represents multiplication. And for matrices multiplication, the number of rows and columns of matrix answer determines by number of rows of first matrix (like G matrix) and number of columns of second matrix (like H matrix).     

Here is more information on matrices multiplication.

That's all for matrix. Feel free to share ideas in the comment below. Thank you!