True or false: scalar multiplication

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   Multiplying a vector by λ changes its magnitude by |λ|.

2. Statement is true

   Yes

   Statement

   A positive λ keeps the direction the same.

3. Statement is true

   Yes

   Statement

   A negative λ reverses the direction.

4. Statement is true

   No

   Statement

   Multiplying by a scalar turns a vector into a number.

5. Statement is true

   Yes

   Statement

   Multiplying by λ = 1 leaves the vector unchanged.

Explanation