# For what value of #lamda# the following vectors will form a basis for #E^3# #a_1 = (1,5,3) , a_2 = (4,0,lamda) , a_3 = (1,0,0) # ?

##### 1 Answer

#### Explanation:

Let the set

form a **Basis** for the **vector space**

Then an **arbitrary vector** **uniquely** be

represented as a **linear combination** of the vectors in

In other words,

Now,

By the **equality of vectors,** then, we have,

In order that this **system of eqns.** may have a **unique soln.,**

we know from **Algebra** that,

Hence, **any non zero real number.**