Linear Combinations

Adjust the scaling factors s₁ and s₂. Observe how combinations of independent vectors span the entire plane, while dependent vectors are trapped on a single line.

x₁ =
1.02.0
x₂ =
3.01.0

Linear Combination (z)

s₁ = 1.0
s₂ = 1.0
z = 1.0
1.02.0
+ 1.0
3.01.0
=
4.03.0

Any zi ∈ ℝ² can be written as a unique linear combination of x₁ and x₂.

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Linear Algebra for Computer Science

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