# Non-pivot columns are linear combinations of the pivot columns.

#### HelpNeeder

##### New member
Nonpivot-columns of a matrix A are linear combinations of the pivot-columns of A.

Could someone explain to me why this is true? Thank you.

#### Subhotosh Khan

##### Super Moderator
Staff member
Nonpivot-columns of a matrix A are linear combinations of the pivot-columns of A.

Could someone explain to me why this is true? Thank you.
Please tell us the definition of a
Pivot Column of a matrix.​

#### HelpNeeder

##### New member
If a matrix is in row-echelon form, then the first nonzero entry of each row is called a pivot, and the columns in which pivots appear are called pivot columns.

#### Jomo

##### Elite Member
That is the correct definition.
Now why do some columns not have pivots? Think hard about this. Look at concrete examples and see if the columns that do not have a pivot in them are in fact linear combinations of the columns that do have pivots in them. After looking at a few examples think about why this happens.

Please post back showing us the work you did for a couple of matrices like I asked for above. Include your reason why you think this happens. If you do not see why, then we'll give you another hint.