the points on the common line

if the system has at least one solution we call it as

if the system has no solutions we call it as

if we have 3 planes and all of these planes are in parallel we have

if we have 3 planes and 2 of these planes are in parallel, we have

if we have 3 planes and there’s no common intersection, we have

if we have 3 planes and they all intersect each other but there’s no common intersection, we have

if we have 3 planes, 2 of them are coincident and they are parallel to the third, we have

if we have 3 planes and the intersection of them is one point, we have

if we have 3 planes and the intersection of them is a line, we have

if we have 3 planes and they are all coincident, we have

if we have 3 planes and their intersection is a plane, we have

Every system of linear equations has zero, one or infinitely many solutions. There are no other possibilities

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