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Lesson 16: Final Review & Comprehensive Practice

Final Review – Linear Algebra Basics (Vectors & Matrices)

Congratulations! You’ve completed the full beginner course.

Here is a quick summary of the main concepts:

Now let’s practice everything together!

Exercise 1

Mixed review – fill in the blanks:

Magnitude of \(\begin{pmatrix} 6 \\ 8 \end{pmatrix}\) =
Unit vector in that direction = \(\begin{pmatrix} x \\ y \end{pmatrix}\), such that \(x = \) and \(y = \)
Dot product with \(\begin{pmatrix} 3 \\ -4 \end{pmatrix}\):

Exercise 2

Match the concept to its definition / property (drag to first empty zone):

Basis → Drop here
Rank → Drop here
Determinant = 0 → Drop here
Eigenvector → Drop here
Click / tap any item to place it in the first empty zone:
Minimal linearly independent spanning set
Number of pivots in row echelon form
Matrix is singular / not invertible
Direction unchanged under transformation (scaled by λ)

Exercise 3

Which statements are true? (Select all that apply)

Final Advice

You now have the foundation for:

Practice problems daily. Try implementing small programs (Python/NumPy) to visualize vectors and transformations.

Thank you for completing the course! You’re ready to tackle more advanced topics.

Keep learning — you’ve got this!

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