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Null Space 3: Relation to Linear Independence
Null Space and Column Space Basis
Point distance to plane
Preimage and Kernel Example
Preimage of a set
Proof of the Cauchy-Schwarz Inequality
Proof: Any subspace basis has same number of elements
Proof: Invertibility implies a unique solution to f(x)=y
Proof: Relationship between cross product and sin of angle
Proving Vector Dot Product Properties
Relating invertibility to being onto and one-to-one
Rotation in R3 around the X-axis
Showing relation between basis cols and pivot cols
Showing that the candidate basis does span C(A)
Singular Matrices
Solving 3 Equations with 3 Unknowns
Span and Linear Independence Example
Sums and Scalar Multiples of Linear Transformations
Surjective (onto) and Injective (one-to-one) functions
Unit Vectors
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