Have you ever thought why is it significant to study eigen values and eigen vectors of a square matrix and what do they mean really?Generally,most of the teachers tend to give formulas for finding them but fail to explain what really are we doing. So what students do is cram those formulas and properties and just blind-foldedly apply them in the exams without knowing the actual concepts which is the real reason why students tend to struggle with maths. This image attached explains the full concept behind eigen values,eigen vectors and characteristic equation. After going through this, I am sure that you won't have to cram a single formula and concept will be crystal clear.
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