To calculate $2A - 5B$, we first compute $2A$ and $5B$, and then subtract $5B$ from $2A$.

Given:

• $A = (1, -3, 7)$
• $B = (3, 4, -5)$

Step 1: Compute $2A$

$2A = 2 \cdot (1, -3, 7) = (2 \cdot 1, 2 \cdot -3, 2 \cdot 7) = (2, -6, 14)$

Step 2: Compute $5B$

$5B = 5 \cdot (3, 4, -5) = (5 \cdot 3, 5 \cdot 4, 5 \cdot -5) = (15, 20, -25)$

Step 3: Compute $2A - 5B$

$2A - 5B = (2, -6, 14) - (15, 20, -25)$ $2A - 5B = (2 - 15, -6 - 20, 14 - (-25)) = (-13, -26, 39)$

Final Result:

$2A - 5B = (-13, -26, 39)$

Let me know if you need further clarifications or detailed explanations!

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1. What is a vector and how do scalar multiplications work?
2. How can this calculation be visualized geometrically?
3. What are practical applications of vector operations like this?
4. How do you perform operations on vectors of different dimensions?
5. Why is it important to maintain consistency in vector dimensions during calculations?

Tip: Always double-check your calculations step-by-step, especially when working with