Prove that if the set of vectors {u1, u2, u3} is linearly dependent and u4 is any vector, then the set {u1, u2, u3, u4} is linearly dependent.

Answer with Step-by-step explanation:

We are given that the set of vectors is lineraly dependent set .

We have to prove that the set is linearly dependent .

Linearly dependent vectors : If the vectors

are linearly  dependent therefore the linear combination

Then ,there exit a scalar which is not equal to zero .

Let then the vector will be zero and remaining  other vectors are not zero.

Proof:

When are linearly dependent vectors therefore, linear combination of vectors of given set

By definition of linearly dependent vector

There exist a scalar which is not equal to zero.

Suppose then  

The linear combination of the set

When

Therefore,the set is linearly dependent because it contain a vector which is zero.

Hence, proved .

there would be 365 different 4 digit numbers

step-by-step explanation:

i belive that it is 365 because i asked google