Understanding Homogeneous Equations in Linear Algebra
Learn about homogeneous equations in linear algebra, including general solutions, matrix algebra concepts, and solving systems of equations with multiple examples and visual aids. Explore the properties of second-order linear homogeneous differential equations and their solutions in this comprehensive guide.
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Presentation Transcript
General solution of 2nd order Linear Homogenous DE is a linear combination of 2 linearly independent functions (which are solutions).
Recall from matrix algebra that Ax = b is a homogeneous equation iff b = 0. Suppose A has 2 free variables. Then the general solution to the homogenous matrix equation Ax = 0 will be of the form x =c1v1 + c2v2.
Recall from matrix algebra that Ax = b is a homogeneous equation iff b = 0. Suppose A has 2 free variables. Then the general solution to the homogenous matrix equation Ax = 0 will be of the form x =c1v1 + c2v2.
