What is the difference between linear and homogeneous systems of equations?

In summary, a linear system of algebraic equations involves variables occurring to the first power, while a homogeneous system of equations has all variables on one side and all constants on the other side, with the constants being zero. The "algebraic" aspect is not necessary for a linear system, which can also be nonlinear.
  • #1
lorik
39
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Homework Statement



I've been struggling for the past hours and can't find the difference between "linear system of algebric equation " and "homogenus system of equation" ,I have the oral(writting) exam tuesday and I would appreciate a little help since I passed writting exam and only final oral would grant me passage to next semester so Id get rid of so many months of suffering .Thanks all
 
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  • #2
The word 'homogeneous' entails that all constant terms are zero, which is not required for an algebraic equation.
 
  • #3
In a linear system of equations, the variables all occur to the first power, as in this example

x + 2y + 3z = 4
-x + 3y -z = 8

I'm not sure what the "algebraic" part contributes.

In a homogeneous system of equations, all the variables are on one side of each equation and the constants on the right side are all zero, as in

x + 2y + 3z = 0
-x + 3y -z = 0

Now, since it wasn't specified that these are linear equations, we could have systems like this

x2 + 2sin(y) + 3z1/2 = 0
-x + 3cos(y) - 1/z = 0

This is a homogeneous system of nonlinear equations.

Hope that helps.
 

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"Difference hard to notice" refers to a situation where two things or concepts appear to be very similar or nearly identical, making it difficult to distinguish any noticeable differences between them.

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Being aware of differences that are hard to notice is important because it allows us to fully understand and appreciate the nuances and complexities of the world around us. It also helps us to avoid making assumptions or generalizations based on surface-level similarities.

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There are several factors that can contribute to differences being hard to notice, such as the level of detail being observed, the complexity of the subject matter, and personal biases or preconceived notions.

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One way to overcome the difficulty of noticing differences is to approach the subject matter with an open and curious mindset, actively seeking out and paying attention to even the smallest details. Engaging in critical thinking and seeking out diverse perspectives can also help to uncover hidden differences.

5. What role does attention to detail play in noticing differences?

Attention to detail is crucial in noticing differences because it allows us to pick up on subtle nuances and variations that may not be immediately obvious. Without paying close attention, it is easy to overlook or dismiss important differences that may exist.

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