Chapter 1.1 Flashcards
A linear equation where the constant term is zero.
A homogeneous linear equation.
A sum of variabels with coefficients that equals e constant without any products roots or functions of the variables.
A linear equation
A solution to a linear system written on the form (s1, s2, … , sn)
An ordered n-tuple.
A finite set of linear equations.
A linear system.
The possible amount of solutions a linear system can have.
Zero, one or infinately many.
Two things that define a linear system with no solutions.
a) At least one equation have all coefficients set to 0 equalling a non-zero constant, after gauss-jordan elimination.
b) The linear equations have no common intersection.
Two things that define a linear system with one solution.
a) Gauss-jordan elimination returns the identity matrix.
b) The linear equations intersect at a point.
Two things that define a linear system with infinitaly many solutions.
a) After gauss-jordan elimination at least one variable have to be expressed by a function of at least one other variable.
b) The common intersection is a subspace of order n>1.
A linear system expressed through a rectangular array.
An augumented matrix.
The three elementary row operations.
a) Multiply a row through a nonzero constant.
b) Interchange two rows.
c) Add a constant times one row to another.
