<jupyter_start><jupyter_text>Linear Algebra- Linear Combinations & Span  Linear Combination & Span- two vectors v and w- linear combination a * v + b * w- linear dependency and independency v = a * w or v != a * w- span all possible vectors u = a * v + b * w- basis vectors i and j  Linear Transformation- linear transformation as a function v - vector , L(v) = output vector- space transformation two basis vectors of a matrix![image.png](attachment:9eddadbb-bcfc-488e-a595-e7851c76ba3f.png)![image.png](attachment:4fbb3b38-395d-426d-b8c8-48f67671e5ad.png)![image.png](attachment:f8ef4be8-c944-4c28-8bcc-ec8e0eb47459.png)![image.png](attachment:d8a3476d-2952-489c-afa0-2a855a87accd.png)![image.png](attachment:c8561090-746c-463f-b905-6bda62b51429.png)  Eigenvectors, Eigenvalues and Eigenbasis<jupyter_code>import numpy as np

A = np.array([[3, 1],[0, 2]])<jupyter_output><empty_output><jupyter_text>Determinant<jupyter_code>import plotly.graph_objects as go

fig = go.Figure(go.Scatter(x=[0,1,4,3,0], y=[0,2,2,0,0], fill="toself"))
fig.show()
np.linalg.det(A)
w, v = np.linalg.eig(A)
w, v
np.dot(A, [-1, 1])
np.det()<jupyter_output><empty_output>
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