Question

If a, b and c are three non-zero, non-coplanar vectors, prove that any vector r in space can be uniquely expressed as a linear combination of a, b, c.​

Answer 1

Answer:

l1 = l2, m1 = m2 and n1 = n2

Step-by-step explanation:

From the above question,

a, b and c are three non-zero, non-coplanar vectors, prove that any vector r in space can be uniquely expressed as a linear combination of a, b, c.​

There exists l,m,n∈R such that la+mb+nc=0

Linear combination:

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.

A linear combination of two or more vectors is the vector obtained by adding two or more vectors (with different directions) which are multiplied by scalar values. The above equation shows that the vector is formed when two times vector is added to three times the vector .

This also means that if,

l1a + m1b + n1c = l2a + m2b + n2c

Then, l1 = l2, m1 = m2 and n1 = n2

Hence, any vector r in space can be uniquely expressed as a linear combination of a, b, c.

For more related question : https://brainly.in/question/32758654

#SPJ1