Find the sum of the given vectors: $\mathbf{a} = \langle 2, -1 \rangle, \quad \mathbf{b} = \langle -1, 7 \rangle$.

Neetesh Kumar | December 18, 2024

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This is the solution to Math 1C
Assignment: 12.2 Question Number 5
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Step-by-step solution:

The sum of two vectors $\mathbf{a}$ and $\mathbf{b}$ is calculated by adding their corresponding components. The formula is:

$\mathbf{a} + \mathbf{b} = \langle a_1 + b_1, a_2 + b_2 \rangle.$

Step 1: Add the components:

Given:

• $\mathbf{a} = \langle 2, -1 \rangle$,
• $\mathbf{b} = \langle -1, 7 \rangle$.

Add the corresponding components:

$\mathbf{a} + \mathbf{b} = \langle 2 + (-1), -1 + 7 \rangle.$

Simplify each component:

$\mathbf{a} + \mathbf{b} = \langle 1, 6 \rangle.$

Final Answer:

The sum of the given vectors is:

$\mathbf{a} + \mathbf{b} = \boxed{\langle 1, 6 \rangle}$

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