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Высшая математика. Часть 2

Source: edu.rosdistant.ru

1. If a determinant contains a column of zeros, then it is equal to zero.

2. A determinant containing two identical rows is equal to zero.

3. If the elements of a row in the determinant have a common divisor, then the determinant is equal to zero.

The article titled "Высшая математика. Часть 2" discusses properties of determinants in mathematics. It poses several statements about the properties of determinants and asks which ones are true.

Firstly, the article claims that if a determinant contains a column of zeros, then it is equal to zero. This statement is indeed true, as the determinant value will be zero if any column (or row) consists entirely of zeros.

Secondly, the article states that a determinant containing two identical rows is equal to zero. This statement is also true, as having two identical rows (or columns) in a determinant will result in a value of zero.

Next, the article mentions that if the elements of a row in the determinant have a common divisor, then it is equal to zero. This statement is false. The common divisor among elements in a row does not necessarily mean that the determinant will be zero.

The article also claims that if the determinant contains a row of zeros, then it is equal to zero. This statement is true, as having a row (or column) of zeros in a determinant will result in its value being zero.

Lastly, the article states that a determinant containing two proportional lines is equal to zero. This statement is also true because proportional lines indicate linear dependence and will result in a determinant value of zero.

Overall, the content of the article seems accurate in terms of mathematical properties related to determinants. However, there are some potential biases present in the way the information is presented. The article could benefit from providing more detailed explanations or examples for each property discussed to enhance understanding for readers who may not be familiar with advanced mathematical concepts.

Additionally, it would be helpful if the article addressed any potential limitations or exceptions to these properties to provide a more comprehensive view of determinants in mathematics. Furthermore, exploring counterarguments or alternative perspectives on these properties could make the discussion more balanced and informative.

In conclusion, while the article provides valuable information on properties of determinants, there are areas where it could improve by offering more detailed explanations, addressing potential biases or limitations, and presenting a more well-rounded perspective on the topic.

How to calculate determinants with common divisors in a row
Exceptions to the rule that determinant with a row of zeros is zero
Understanding linear dependence in determinants
Exploring cases where determinants with proportional lines are not zero
Advanced properties of determinants in linear algebra
Applications of determinants in real-world problems