Matrices operations theory

Matrices additions and subtractions theory

 

The sum of two Matrices (Aij), (Bij) of the same dimension, is another matrix (Rij) of the same dimension and with generic term sij=aij+bij.

 

Therefore, to be able to add two matrices, they must have the same dimension

 

Addition of Matrices: (Aij) + (Bij) = (Aij + Bij)

 

Subtraction of Matrices: (Aij) – (Bij) = (Aij – Bij)

 

 

Example:

Bioprofe |Exams with exercises about physics, chemistry and mathematics | Matrices

Bioprofe |Matrices operations theory|01

 
 

Matrix multiplications and division theory

 

For two matrices A and B can be multiplied, A · B, it is necessary that the number of columns in the first matrix be the same as the number of rows in the second one.

In this case, the product A · B = C is another matrix whose elements are obtained by multiplying each row of the first matrix by each column of the second vector, as follows:

Aik·Bkj=Cij

The resulting matrix C has many rows as A and many columns as B

Example:

Bioprofe |Exams with exercises about physics, chemistry and mathematics | Matrices

Bioprofe |Matrices operations theory|02

Bioprofe |Exams with exercises about physics, chemistry and mathematics | Matrices

Bioprofe |Matrices operations theory|03

 

The matrix division is defined as the product of the numerator multiplied by the inverse matrix of the denominator. That is to say:

A/B = A·B-1

To multiply a number by a matrix it is multiplied the number by each matrix digit.

Example:

Bioprofe |Exams with exercises about physics, chemistry and mathematics | Matrices

Bioprofe |Matrices operations theory|04

 

To divide a matrix by a number all the terms of the matrix are divided by the number.

Example:

Bioprofe |Exams with exercises about physics, chemistry and mathematics | Matrices

Bioprofe |Matrices operations theory|05

 

 

 

 

You can download the App BioProfe READER to practice this theory with self-corrected exercises.

 

 

Books that we recommend to extend knowledge of the subject

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