Find the Norm [[-2],[2],[1]]

Problem

‖[−2],[2],[1]‖

Solution

1. Identify the components of the vector v=[[−2],[2],[1]] as (v_1)=−2 (v_2)=2 and (v_3)=1

2. Apply the formula for the Euclidean norm (also known as the L2 norm) of a vector in ℝ3 which is ∥v∥=√(,(v_1)2+(v_2)2+(v_3)2)

3. Substitute the values into the formula:

∥v∥=√(,(−2)2+(2)2+(1)2)

4. Square each component:

∥v∥=√(,4+4+1)

5. Sum the squared values:

∥v∥=√(,9)

6. Simplify the square root to find the final magnitude.

Final Answer

‖[−2],[2],[1]‖=3

Want more problems? Check here!