Independent equation

The equations x − 2y = −1, 3x + 5y = 8, and 4x + 3y = 7 are linearly dependent, because 1 times the first equation plus 1 times the second equation reproduces the third equation. But any two of them are independent of each other, since any constant times one of them fails to reproduce the other.

The equations 3x + 2y = 6 and 3x + 2y = 12 are independent, because any constant times one of them fails to produce the other one.

A system of three linearly independent equations, y=x+1, y=–2x+1, and y=3x–2. There are no two constants a and b such that a times the first equation plus b times the second equation equals the third equation.

An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. The concept typically arises in the context of linear equations. If it is possible to duplicate one of the equations in a system by multiplying each of the other equations by some number (potentially a different number for each equation) and summing the resulting equations, then that equation is dependent on the others. But if this is not possible, then that equation is independent of the others.

单词	Independent equation
释义	Independent equation 英语百科 Independent equation An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. The concept typically arises in the context of linear equations. If it is possible to duplicate one of the equations in a system by multiplying each of the other equations by some number (potentially a different number for each equation) and summing the resulting equations, then that equation is dependent on the others. But if this is not possible, then that equation is independent of the others.
随便看	radial shrinkage的意思 radial shuffling of fuel的意思 radial site的意思 radial sleeve bearing的意思 radial sliding bearing的意思 radial slit的意思 radial slit domain的意思 radial slot的意思 radial solid mixing的意思 radial space的意思 radial spacing的意思 radial spar的意思 radial spectrum的意思 radial spherical roller bearing的意思 radial spherulite的意思 radial sphincterotomy的意思 radial spill strip的意思 radial spine的意思 radial split的意思 Radial spoke的意思 radial spoke artifact的意思 radial spoke fan的意思 radial spread的意思 radials shied的意思 radial stability的意思