Answer to Question #298581 in Linear Algebra for shahana

Question

determine whether the statement is true or false, and justify your answer.b) If an elementary row operation is applied to a matrix that is in row echelon form, the resulting matrix will still be in row echelon form.c) Every matrix has a unique row echelon form.d) A homogeneous linear system in n unknowns whose corresponding augmented matrix has a reduced row echelon form with r leading 1’s has n − r free variables.e) All leading 1’s in a matrix in row echelon form must occur in different columns.f) If every column of a matrix in row echelon form has a leading 1, then all entries that are not leading 1’s are zero.g) If a homogeneous linear system of n equations in n unknowns has a corresponding augmented matrix with a reduced row echelon form containing n leading 1’s, then the linear system has only the trivial solution. i) If a linear system has more unknowns than equations, then it must have infinitely many solutions