In university, students who study differential equations will learn homogeneous linear regression and nonhomogeneous linear equations. It is difficult to solve nonhomogeneous linear equations. Next, we will teach you how to use matrices to solve nonhomogeneous linear equations.

Tools/materials

nbsp？ Differential equation knowledge

operational approach

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Next, I will explain it to you with examples. Let's look at the topic first and find all the solutions of the following nonhomogeneous linear equations.

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Firstly, write the augmented matrix of non-homogeneous linear equation, as shown in the figure below.

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Then the roof will be enhanced with Huawei ladder matrix, as shown in the figure below.

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Next, we start to take the free element and make it 0, and get the special solution X0 of ax = b.

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Then let one of the free elements be 1 and the others be 0, and the basic system of AX=0 can be obtained.

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Finally, just write a general solution.