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hahatyshka
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how can i show that a determinant is divisible by a number, without directly evaluating the determinant?
Determinant Divisibility: Learn How to Show Without Evaluation
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To demonstrate that a determinant is divisible by a specific number without direct evaluation, one effective approach is to work modulo that number. This method allows for the application of various techniques to show that the determinant equals zero under the chosen modulus. Participants emphasize the importance of understanding properties of determinants, such as linearity and row operations, which can simplify the process. Additionally, leveraging known results about specific matrix structures can aid in proving divisibility. Ultimately, using modular arithmetic provides a powerful tool for addressing determinant divisibility.
Hello!
In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way:
I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true?
And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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