Advanced Algebra
Vectors and Matrices
Point the way with vectors — then let matrices move the whole plane at once.
THE SYLLABUS
I
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Vectors
Start
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Vector Addition
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Drawing Vectors
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Component-Wise Addition
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Level Review
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II
🔒 5 lessons
🔒 Arrows with length and direction — add them tip-to-tail and see why order never matters.
III
🔒 5 lessons
🔒 Flip a vector to subtract it — the arrow that connects any two points.
IV
🔒 8 lessons
🔒 Stretch and combine vectors to reach any point in the plane.
V
🔒 6 lessons
🔒 Measure a vector: its length from the Pythagorean theorem, its direction from an angle.
VI
🔒 4 lessons
🔒 Turn an angle and a length into exact x- and y-components with sine and cosine.
VII
🔒 6 lessons
🔒 Planes in crosswinds and boats on rivers — add real velocities like a navigator.
VIII
🔒 6 lessons
🔒 Meet the dot product on unit vectors — the number that says how aligned two directions are.
IX
🔒 7 lessons
🔒 The full dot product: lengths, angles, and the test for perpendicular vectors.
X
🔒 4 lessons
🔒 Work backwards — find the combination of building blocks that produces a given vector.
🔒 7 lessons
🔒 Transform vectors with rules — and discover the special rules that keep lines straight.
🔒 8 lessons
🔒 A matrix is a machine that moves every vector at once — read it by where it sends the basis.
🔒 5 lessons
🔒 Add, subtract, and scale matrices — arithmetic on whole transformations.
🔒 5 lessons
🔒 Multiply matrices row-by-column and see why the order of multiplication matters.
🔒 5 lessons
🔒 Chain transformations together — one matrix that does two jobs at once.
🔒 7 lessons
🔒 The determinant: the single number that measures how a matrix stretches area.
🔒 6 lessons
🔒 Undo a transformation — build the inverse matrix and see when none exists.
🔒 5 lessons
🔒 Solve whole systems of equations in one stroke with matrices and inverses.