To solve the given expression:

$A = (-7) \cdot \left[(-8, 4) + (0, 6)\right]$

1. Simplify the vector addition: Add the corresponding components of the vectors: $(-8, 4) + (0, 6) = (-8 + 0, 4 + 6) = (-8, 10)$

2. Multiply by the scalar $-7$: Multiply each component of the vector $(-8, 10)$ by $-7$: $(-7) \cdot (-8, 10) = (-7 \cdot -8, -7 \cdot 10) = (56, -70)$

Final Answer:

$A = (56, -70)$

Would you like a detailed breakdown or have any questions?

---

Related Questions:

1. How do you calculate the magnitude of a vector like $(56, -70)$?
2. What is the result if the scalar multiplier were positive $7$ instead of $-7$?
3. How do vector operations like addition and scalar multiplication apply in physics?
4. What happens if one of the vectors in the addition is a zero vector?
5. How can you graphically represent scalar multiplication of a vector?

Tip:

When multiplying a vector by a scalar, always remember that the direction of the vector changes if the scalar is negative.