Method of understanding and memorizing Kramer's law of inhomogeneous linear equations and inhomogeneous linear equations
In the non-homogeneous linear equations , there is the definition of Cramer's law, which shows that D = the value of the coefficient determinant aij , x1=D1/D, x2=D2/D...and so on xn=Dn/D, where D1, D2 …Dn is the value of replacing the inhomogeneous term of the inhomogeneous linear equation with the column aij in the coefficient determinant, for example, D1 is replacing the inhomogeneous term with the column a1j.
From this definition, we can understand memory in this way. When the coefficient determinant is not 0, that is, the denominator of x1=D1/D is not 0, then each unknown number of x can be calculated with a corresponding value, which is what the book says D is not equal to 0, and there is a unique solution.
When D-0, because the denominator is equal to 0, the definition of high numbers shows that when the denominator tends to 0 and the numerator is a constant, the limit of this number tends to infinity. That is, the system of equations has infinitely many solutions.
Generalized to homogeneous linear equations , when the homogeneous equations are regarded as non-homogeneous equations , its non-homogeneous term is 0, which is substituted into it like the above-mentioned Kramer's law of non-homogeneous equations To solve it, because the coefficient determinant contains a column vector of 0, the coefficient determinant must be 0, that is, D1 in x1=D1/D must be 0, indicating that no matter what the homogeneous equation system, his D1~Dn will be zero, so we have to discuss his denominator, when the denominator is not zero , there is no doubt that all x are 0, is the equation has only one solution, and the solution is 0 , when the denominator is zero , the limit It can be seen from the definition that the 0 to 0 type is an undetermined formula with infinite possibilities, that is, the equation system has infinite solutions.
This way, it is not easy to confuse Cramer's Law.