MAT1503 Linear Algebra With Complete Solutions
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homogeneous linear equations - x₁ − 2x₂ − 3x₃ + x₄ = 0
solution of a linear system - The element is a solution of each equation
solution set (general solution) - All solutions of a linear system with the number
sequence as the elements
ordered n-tuple - A linear solution written as (a₁, a₂, ... , aⱼ)
ordered pair - ordered n-tuple if n = 2
ordered triple - ordered n-tuple if n = 3
consistent system - A linear system that has at least one solution
equivalent systems - Two systems of equations that have the same solution set
inconsistent system - A linear system that has no solutions
parameter - An assigned arbitrary value where the linear system has infinite
solutions
parametric equations - The solution expressed by the equations using parameters
algebraic operations - 1) Add a multiple of one equation to another
2) Multiply an equation by a nonzero constant
3) Interchange two equations
Elementary Row Operations - 1) Add a multiple of one row to another row
2) Multiply any row by a nonzero constant
3) Interchange two rows
augmented matrix - An abbreviation of a linear system in a rectangular array of
numbers
elementary matrix - A matrix that was (or could be) produced by performing a
single Elementary Row Operation on an identity matrix
identity matrix - A square matrix with 1's on the main diagonal and zeros
everywhere else. Note A×I = A and I×A = A
Row Echelon Form - A matrix that has leading ones on the main diagonal and zeros
below the leading ones.
Reduced Row Echelon Form - A matrix that has leading ones on the main diagonal
and zeros above and below the leading ones.
matrix - A rectangular array of numbers
linear equation in n (j) unknowns - a₁x₁ + a₂x₂ + ... + aⱼxⱼ = b
linear equation - x + 3y = 7 or x₁ − 2x₂ − 3x₃ + x₄ = -1 (no products or roots of
variables)
system of linear equations (linear system) - A finite set of linear equations
solution of a linear equation - A sequence of numbers for which the substitution
with variables will make the equation a true statement
leading variables - The variables corresponding to the leading 1's in the augmented
matrix
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