Question

An example of a linear combination of vectors a and b is the vector c, where c = ma + nb. What are the values of m and n?

Answer 1

In a linear combination of vectors a and b, the values of m and n can be any real numbers that satisfy the equation c = ma + nb. They determine how much of each vector is added to create the resulting vector c.

Step-by-step explanation:

In a linear combination of vectors a and b, the vector c can be expressed as c = ma + nb, where m and n are scalars. The values of m and n can be any real numbers that satisfy the equation. They determine how much of each vector is added to create the resulting vector c.

For example, if m = 2 and n = 3, the linear combination would be c = 2a + 3b. This means that vector c is formed by adding 2 times the magnitude of vector a to 3 times the magnitude of vector b.

Note that there are infinitely many possible values of m and n that can satisfy the equation, as long as they are real numbers.