In mathematics, the assembling of expressions is the key. Regarding any mathematics calculation, the proper assembling of the procedure or step is the significant rule one must obey. The most highlighted assembled tool in mathematics is known as Matrix.
What is a Matrix?
Discussing the matrix, it is the most assembled and well-organized state of calculation in mathematics. It is a rectangular array with columns and rows of numbers, digits, or signs. We call the equation of the matrix by the number of columns and rows, making a rectangular arrangement.
As an example
[ 1 9 − 13
20 5 − 6 ]
We have two rows and three columns here hence the dimension of the matrix would be 2x3 or two by three.
Conformable matrix
In mathematics, a matrix is a Conformable matrix if it has suitable dimensions that it can follow the defining operations, i.e., addition, multiplication, etc.
If the provided values of the dimensions (rows and columns) are the same as two rows and two columns, it is a conformable matrix. It can follow the multiplication, addition, and subtraction rules.
To obey the basic mathematical rules of multiplication, addition, all we need is the same number of columns and rows of a matrix. In mathematics, matrix multiplication is only possible if the given number of columns in the first matrix needs to be equal to the number of rows in the second matrix. The matrix product is its final result with the same number of columns in first as the number of rows present in the second matrix.
A . B =C
C = A . B
How to calculate the matrix?
As mentioned above, to add or multiply, we need to know the number of rows and columns arranged in the matrix.
For addition matrix
[3,8] + [4,2]
[4,6] + [1,-2]
To add two matrices, add the numbers in the common position on both the first and second matrix.
The calculations would be
(taken from the first row of the first matrix) + (from the first row of the second matrix)=3 + 4= 7
(taken from the second row of the first matrix)+(from the second row of the second matrix) =8 +2=10
(same positions as the above)=4 + 1= 5
(same positions on the matrix)=6 − 2=4
The above two matrices are the same in size, i.e., the rows and the columns have a matching size of two rows and two columns.
Multiply matrix
To multiply a single set of the matrix, it can be easy as it just multiplied with a single digit.
2x [2,4] [4,6]
=[ 2x2, 2x4]
[2x4, 2x6]
=[4,8]
[8,12]
Multiply a matrix with a matrix
Here we follow the Dot product rule. Where we multiply the same numbers
[2,5,3] [4,0]
x
[3,6,2] [5,7]
[2,3]
So, we multiply [2,5,3] x [4,5,2], [2,5,3]x[0,7,3] and [3,6,2]x[4,5,2], [3,6,2] x [0,7,3].
Multiplication matrix has numerous applications in various fields of science like physics, applied math, statistics, and engineering.
What is a factor in mathematics?
It is an algebraic expression. A factor in mathematics is a number that can be multiplied to another number. Whereas, a number has many factors, multiplying with the factor of any other number.
Factor x Factor= Number
2 x 4=8, so 2 and 4 are factors of 8.
4 x 2=8 are also factors of 8.
1 x 8=8, here 1 and 8 are the factors of number 8.
So, 2, 4, 1, and 8 are all the factors of number 8. The factors with negative signs are also known as the factors of the same number as positive factors, i.e., -2, -4, -8,-1 are also the factors of -8.
Algebraic expression of factor
While in algebra, the factors are expressed in both digits and alphabets like a, b, or commonly x.
(x,2) x (x,4)= x2 + 8x + 4
Here (x,2) and (x,4) are the factors of the x2+8x+4 algebraic equation.
In mathematics, 12 and 16 are known as the common factors with a range of the same numbers.
Learning the equations and the formulas is not so difficult. If you still find it difficult to memorize the equations and formulas, you can find online help as there are custom and online calculators like matrix calculator and factor calculator which you can use to practice equations on runtime. Online tools would prove best for you to learn and practice.
