Solve systems of linear equations: the two-equation case and what its solutions look like geometrically, writing a system as an augmented matrix, and Gaussian elimination.
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prerequisite lessons
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Lesson 01 · Solving systems of two linear equations
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The 5 lessons in this unit. Expand any one to see what it covers. Each unlocks when its own prerequisites are passed.
01
Solving systems of two linear equations
6 questions
Learn how to represent a system of two linear equations and solve it algebraically using both the substitution and elimination methods to find the values that satisfy both equations simultaneously.
Covers
Understanding and representing systems of linear equations
Solving by substitution
Solving by elimination (addition/subtraction method)
02
Interpreting solutions to systems of two linear equations
5 questions
Learn how to determine whether a system of two linear equations has a unique solution, no solution, or infinitely many solutions by analysing the relationships between their coefficients and interpreting the geometric meaning of each case.
Covers
Interpreting solutions - unique, infinite, and no solution cases
03
Writing systems of equations as augmented matrices
9 questions
Learn how to rewrite a system of linear equations as a matrix equation and as an augmented matrix, and how to convert between augmented matrices and their corresponding systems of equations by matching coefficients and constants to variables in a consistent order.
Covers
From equations to matrix-vector form
Constructing the augmented matrix for a system
Interpreting an augmented matrix as a system of equations
04
Gaussian elimination I: forward elimination
9 questions
Learn how to use elementary row operations to systematically transform an augmented matrix into row echelon form via forward elimination, laying the groundwork for solving systems of linear equations by back substitution.
Covers
Row operations
Row echelon form and row operations
Forward elimination to achieve row echelon form
05
Gaussian elimination II: back substitution and solution types
9 questions
Learn how to use Gaussian elimination by combining forward elimination and back substitution to solve systems of linear equations, and determine whether a system has a unique solution, infinitely many solutions, or no solution from the row echelon form.
Covers
Back substitution from row echelon form
Recognising unique, infinite, and no solutions
Gaussian elimination (forward elimination + back substitution)
This unit is part of our Essential Linear Algebra for ML learning path, which contains 61 lessons. Every one of them is drawn below.
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5 lessons in this unit
26 prerequisite lessons across the unit, counting every step back to the start
30 other lessons in the learning path - after this unit, or alongside it
Builds on: Matrices
Leads to: Matrix transformations, Vectors in Euclidean space
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More in Linear algebra: Vectors in Euclidean space, Matrices, Matrix transformations, Eigenvalues, eigenvectors and singular value decomposition