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Intro to the three properties of linear transformations
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Intro to the three properties of linear transformations
7:08
About this lesson
Properties of Linear Transformation Overview:
The 3 properties of Linear Transformation
• \(T(u+v)=T(u)+T(v)\)
• \(T(cu)=cT(u)\)
• \(T(0)=0\)
• \(T(u+v)=T(u)+T(v)\)
• \(T(cu)=cT(u)\)
• \(T(0)=0\)
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Video 1 of 7
Intro to the three properties of linear transformations
7 min
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Proving a transformation is linear using the superposition property
13 min
Proving a transformation is not linear using the zero vector property
3 min
Proving a transformation with absolute value is not linear
8 min
Proving an affine transformation T(x)=Ax+B is not linear when B≠0
5 min
Proving transformed linearly dependent vectors remain linearly dependent
9 min
Proving T(x) = 0 when T maps all basis vectors to zero
7 min