Mat1503 (Linear Algebra) / Mat1503
Assignment 4 |Complete Answers &
Solutions
matrix - ✔✔✔ANSWER-A rectangular array of numbers
linear equation in n (j) unknowns - ✔✔✔ANSWER-a₁x₁ + a₂x₂ + ... + aⱼxⱼ = b
linear equation - ✔✔✔ANSWER-x + 3y = 7 or x₁ − 2x₂ − 3x₃ + x₄ = -1 (no
products or roots of variables)
,system of linear equations (linear system) - ✔✔✔ANSWER-A finite set of linear
equations
solution of a linear equation - ✔✔✔ANSWER-A sequence of numbers for which
the substitution with variables will make the equation a true statement
homogeneous linear equations - ✔✔✔ANSWER-x₁ − 2x₂ − 3x₃ + x₄ = 0
solution of a linear system - ✔✔✔ANSWER-The element is a solution of each
equation
solution set (general solution) - ✔✔✔ANSWER-All solutions of a linear system
with the number sequence as the elements
ordered n-tuple - ✔✔✔ANSWER-A linear solution written as (a₁, a₂, ... , aⱼ)
ordered pair - ✔✔✔ANSWER-ordered n-tuple if n = 2
ordered triple - ✔✔✔ANSWER-ordered n-tuple if n = 3
consistent system - ✔✔✔ANSWER-A linear system that has at least one solution
equivalent systems - ✔✔✔ANSWER-Two systems of equations that have the same
solution set
, inconsistent system - ✔✔✔ANSWER-A linear system that has no solutions
parameter - ✔✔✔ANSWER-An assigned arbitrary value where the linear system
has infinite solutions
parametric equations - ✔✔✔ANSWER-The solution expressed by the equations
using parameters
algebraic operations - ✔✔✔ANSWER-1) Add a multiple of one equation to another
2) Multiply an equation by a nonzero constant
3) Interchange two equations
Elementary Row Operations - ✔✔✔ANSWER-1) Add a multiple of one row to
another row
2) Multiply any row by a nonzero constant
3) Interchange two rows
augmented matrix - ✔✔✔ANSWER-An abbreviation of a linear system in a
rectangular array of numbers
elementary matrix - ✔✔✔ANSWER-A matrix that was (or could be) produced by
performing a single Elementary Row Operation on an identity matrix
identity matrix - ✔✔✔ANSWER-A square matrix with 1's on the main diagonal
and zeros everywhere else. Note A×I = A and I×A = A
Assignment 4 |Complete Answers &
Solutions
matrix - ✔✔✔ANSWER-A rectangular array of numbers
linear equation in n (j) unknowns - ✔✔✔ANSWER-a₁x₁ + a₂x₂ + ... + aⱼxⱼ = b
linear equation - ✔✔✔ANSWER-x + 3y = 7 or x₁ − 2x₂ − 3x₃ + x₄ = -1 (no
products or roots of variables)
,system of linear equations (linear system) - ✔✔✔ANSWER-A finite set of linear
equations
solution of a linear equation - ✔✔✔ANSWER-A sequence of numbers for which
the substitution with variables will make the equation a true statement
homogeneous linear equations - ✔✔✔ANSWER-x₁ − 2x₂ − 3x₃ + x₄ = 0
solution of a linear system - ✔✔✔ANSWER-The element is a solution of each
equation
solution set (general solution) - ✔✔✔ANSWER-All solutions of a linear system
with the number sequence as the elements
ordered n-tuple - ✔✔✔ANSWER-A linear solution written as (a₁, a₂, ... , aⱼ)
ordered pair - ✔✔✔ANSWER-ordered n-tuple if n = 2
ordered triple - ✔✔✔ANSWER-ordered n-tuple if n = 3
consistent system - ✔✔✔ANSWER-A linear system that has at least one solution
equivalent systems - ✔✔✔ANSWER-Two systems of equations that have the same
solution set
, inconsistent system - ✔✔✔ANSWER-A linear system that has no solutions
parameter - ✔✔✔ANSWER-An assigned arbitrary value where the linear system
has infinite solutions
parametric equations - ✔✔✔ANSWER-The solution expressed by the equations
using parameters
algebraic operations - ✔✔✔ANSWER-1) Add a multiple of one equation to another
2) Multiply an equation by a nonzero constant
3) Interchange two equations
Elementary Row Operations - ✔✔✔ANSWER-1) Add a multiple of one row to
another row
2) Multiply any row by a nonzero constant
3) Interchange two rows
augmented matrix - ✔✔✔ANSWER-An abbreviation of a linear system in a
rectangular array of numbers
elementary matrix - ✔✔✔ANSWER-A matrix that was (or could be) produced by
performing a single Elementary Row Operation on an identity matrix
identity matrix - ✔✔✔ANSWER-A square matrix with 1's on the main diagonal
and zeros everywhere else. Note A×I = A and I×A = A
