Questions: Find the sum of the given vectors. (Simplify your answer completely.) [ mathbfa=[-4,8], quad mathbfb=[8,-2] mathbfa+mathbfb=square ]

Transcript text: Find the sum of the given vectors. (Simplify your answer completely.) \[ \begin{array}{l} \mathbf{a}=[-4,8], \quad \mathbf{b}=[8,-2] \\ \mathbf{a}+\mathbf{b}=\square \end{array} \]

Solution

Solution Steps

Step 1: Understand the problem

We are given two vectors: \[ \mathbf{a} = [-4, 8], \quad \mathbf{b} = [8, -2]. \] We need to find the sum of these two vectors, \(\mathbf{a} + \mathbf{b}\).

Step 2: Add the corresponding components

To add two vectors, we add their corresponding components. That is: \[ \mathbf{a} + \mathbf{b} = [a_1 + b_1, a_2 + b_2]. \] Substituting the given values: \[ \mathbf{a} + \mathbf{b} = [-4 + 8, 8 + (-2)]. \]

Step 3: Simplify the components

Perform the addition for each component: \[ \mathbf{a} + \mathbf{b} = [4, 6]. \]