Linear dependency

2. KHANDAKER MONJIR-UL-MORSALIN
 Id: 171-15-9421
 Department: CSE
 Batch: 46th

3. MATHEMATICS II
Linear Algebra and coordinate geometry

4. PRESENTATION ON
Linear dependency and linear independency

5. LINEARLY DEPENDENT AND LINEARLY
INDEPENDENT
 If one is parallel to other then they are linearly
dependent.
 If one is not parallel to other they then are linearly
independent.

6. IMPORTANT NOTES
 Any set containing a zero vector is linearly
dependent.
 Any two vectors are linearly dependent if one is
scalar multiple of other.
 The non zero rows of a matrix in echelon form are
linearly independent.
 Every singleton having a non zero vector is linearly
independent.
 Any empty set is linearly independent.
 In plane any two non zero vectors are linearly
dependent if they are parallel.
 In plane, any two non zero vectors are linearly
independent if they are intersecting.

7. MATHEMATICAL PROCESS OF CHECKING
LINEAR DEPENDENCY
Step 01 : We have to remind the sets by letters.
Step 02 : We have to write the vectors as column or
row.
Step 03 : We will get a matrix and then we have to
reduce that matrix into echelon form by
elementary row operations.
Step 04 : If we found any zero row in that echelon
formed matrix will linearly dependent. If
we found no zero row will be linearly
independent.

8. LINEAR DEPENDENT RELATION
If the sets are linearly dependent. So from the right
side of the echelon formed matrix
we found a equation and it equals to zero.
Putting sets we found a relation. It is linear
dependence relation.

9. EXPRESSION OF 2ND VECTOR WITH THE HELP
OF OTHERS
From the linear dependence relation we can
express 2nd vector with the help of other vectors.