Linear Algebra Chapter 1, 2, 3
consistent system
a system of linear equations with at least one solution
inconsistent system
a system of linear equations with no solution
row echelon form
a matrix where the leading coefficient of each row is 1 and all entries below the
leading 1 are zero
pivot
the leading 1 in a row of a matrix in row echelon form
reduced row echelon form
a matrix in row echelon form where all entries above the leading 1 are also zero
Gaussian elimination
a method used to transform a matrix into row echelon form
Gauss-Jordan elimination
a method used to transform a matrix into reduced row echelon form
elementary row operations
operations that can be performed on rows of a matrix: 1) interchange two equations,
2) multiply an equation by a nonzero constant, 3) add a multiple of one equation to
another
, homogeneous solution
A system of linear equations having matrix form Ax = O
trivial solution
a homogeneous solution where all variables are equal to zero
row equivalent
when two matrices can be transformed into each other using elementary row
operations
matrix
a rectangular array of numbers
column matrix
a matrix with only one column
column vector
a column matrix
row vector
a matrix with only one row
equality of matrices
two matrices are equal if they have the same size and corresponding entries are
equal
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