Title Linear Combination _01.pdf ✅

Page 2 of 8 Linear combination and Linear Dependency A vector is called a linear combination of vectors if it can be expressed in the following form: ( ) ( ) ( ) ( ) Here are scalars. If , then the above equation will be reduce to . It implies is a linear combination of single vector if is a scalar multiple of . Consider: ( ) ( ). We evaluate the coefficients of where There exists no linear combination if there is no solution of the system (when the system is inconsistent). Example: consider the vectors ( ) ( ) ( ) in (three dimensional vector space). Show that ( ) is a linear combination of Solution: In order to show that is a linear combination of there must be scalars in a vector field such that ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )