1. **State the problem:** Simplify the expression $$7[3 -2 1] - \frac{1}{3} [21 6 -9]$$ where the brackets denote scalar multiplication of each element in the vector. 2. **Apply scalar multiplication:** Multiply each element inside the brackets by the scalar outside. $$7[3 -2 1] = [7 \times 3, 7 \times (-2), 7 \times 1] = [21, -14, 7]$$ $$\frac{1}{3}[21 6 -9] = \left[\frac{1}{3} \times 21, \frac{1}{3} \times 6, \frac{1}{3} \times (-9)\right] = [7, 2, -3]$$ 3. **Subtract the two resulting vectors element-wise:** $$[21, -14, 7] - [7, 2, -3] = [21 - 7, -14 - 2, 7 - (-3)] = [14, -16, 10]$$ 4. **Final answer:** $$[14, -16, 10]$$