if we have parametric equations at the end of solving the linear system that means that we have (not sure about this one .. check it in the book)

matrix A mxn, we have .. of rows and .. of columns

elementary row operations on a matrix

in achieving row-echelon form is that if a row doesn’t consist entirely of zeros, then the first nonzero number in the row is ..

in achieving row-echelon form is that if there are any rows that consists entirely of zeros, then they are grouped together at the bottom of the matrix

in achieving row-echelon form is that in any two successive rows that don’t consist entirely of zeros, the leading one in the lower row occurs further to the … than the leading one in the higher row

Each column that contains a leading one has zeros everywhere else in that column

A matrix of row-echelon form can be called a reduced row-echelon form

A matrix of reduced row-echelon form can be called a row-echelon form

A system of linear equations with all constant terms are 0

x1 = 0, x2 = 0, x3 = 0

homogeneous system is always consistent

nontrivial solution in homogeneous system means that the system has trivial solution in addition to infinitely many solutions

to say that A = B we have to achieve

The m x n matrix of all entries are equal to zero is called …

A + B = B + A

(A + B) + C = A + (B + C)

K(A + B) = KA + KB

A + 0 = 0 + A = A

A column vector

A row vector