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Courses  /  Advanced Algebra  /  Vectors and Matrices
Advanced Algebra
Vectors and Matrices

Vectors and Matrices

Point the way with vectors — then let matrices move the whole plane at once.
17 levels 99 lessons ~11 hours Intermediate Taught by Newton 0 of 99 complete
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THE SYLLABUS dev · all lessons unlocked
I
Vectors

0 / 5
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Vectors
Free
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Vector Addition
Open
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Drawing Vectors
Open
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Component-Wise Addition
Open
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Level Review
Open
II
Vector Subtraction

0 / 5
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Opposite Vectors
Open
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Vector Subtraction
Open
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Drawing Differences
Open
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Vector Differences
Open
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Level 2 Review
Open
III
Linear Combinations

0 / 8
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Scalar Multiplication
Open
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Reversing Direction
Open
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Linear Combinations
Open
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Linear Combination Grids
Open
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Solving Linear Combinations
Open
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Drawing Linear Combinations
Open
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Linear Interpolation
Open
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Level Review
Open
IV
Magnitude and Direction

0 / 6
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Magnitude and Direction
Open
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Drawing from Polar Form
Open
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Polar Angles
Open
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Finding the Polar Angle
Open
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Computing from Components
Open
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Level Review
Open
V
Components from Angles

0 / 4
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Vector Components
Open
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Non-Polar Angles
Open
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Combining Vectors
Open
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Level 5 Review
Open
VI
Combining Velocities

0 / 6
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Adding Velocities
Open
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Velocity Magnitude and Direction
Open
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Velocity from Bearing
Open
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Combining Velocity Bearings
Open
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Relative Velocity
Open
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Level 6 Review
Open
VII
Unit Vector Dot Products

0 / 6
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Scaling and Magnitude
Open
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Unit Vectors
Open
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Comparing Unit Vectors
Open
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The Dot Product
Open
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Unit Vector Dot Products
Open
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Level Review
Open
VIII
General Dot Products

0 / 7
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General Dot Products
Open
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Scaling Dot Products
Open
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Dot Product from Magnitudes
Open
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Angle from Dot Product
Open
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Self Dot Products
Open
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Orthogonal Dot Products
Open
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Dot Products — Level Review
Open
IX
Vectors from Combinations

0 / 4
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Vectors from Combinations
Open
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Possible Combinations
Open
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Standard Basis Vectors
Open
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Level Review
Open
X
Transforming Vectors

0 / 7
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Transforming Vectors
Open
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Transforming Basis Vectors
Open
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Linear Transformations
Open
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Transforming Combinations
Open
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Plotting Transformed Vectors
Open
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Non-Integer Combinations
Open
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Level Review
Open
Matrices

0 / 8
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Matrices as Transformations
Open
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Transforming via Matrices
Open
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Transforming Shapes
Open
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Diagonal Matrices
Open
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Rotations and Reflections
Open
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Shear Transformations
Open
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Degenerate Transformations
Open
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Matrices Review
Open
Matrix Operations

0 / 5
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Matrix-Vector Multiplication
Open
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Matrix as Multiple Vectors
Open
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Matrix Addition and Subtraction
Open
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Scalar Matrix Multiplication
Open
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Matrix Operations Review
Open
Matrix Multiplication

0 / 5
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Matrix Multiplication
Open
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Matrix Dimensions
Open
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Sizing and Multiplying
Open
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The Identity Matrix
Open
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Level Review
Open
Matrix Composition

0 / 5
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Multiple Transformations
Open
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Composing Transformations
Open
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Composing by Multiplying
Open
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Squaring and Cubing
Open
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Level Review
Open
Determinants

0 / 7
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Transformed Areas
Open
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Determinant of a Triangular Matrix
Open
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Determinant of any 2×2 Matrix
Open
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Computing Determinants
Open
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Determinant 0
Open
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Negative Determinants
Open
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Level Review
Open
Inverse Matrices

0 / 6
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The Inverse Matrix
Open
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Producing the Identity
Open
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Inverting a Matrix
Open
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Computing the Inverse Matrix
Open
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Non-invertible Matrices
Open
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Level Review
Open
Systems of Equations

0 / 5
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Systems of Equations
Open
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Matrices as Systems of Equations
Open
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Solving Systems of Equations
Open
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Solving with Inverses
Open
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Level Review
Open