1. **State the problem:** Calculate the estimated file size for a 512x512 matrix with a bit depth of 6. 2. **Formula:** The file size in bits is given by $$\text{File size} = \text{width} \times \text{height} \times \text{bit depth}$$ 3. **Apply the formula:** $$512 \times 512 \times 6$$ 4. **Calculate:** $$512 \times 512 = 262144$$ $$262144 \times 6 = 1572864 \text{ bits}$$ 5. **Convert bits to bytes:** $$\frac{1572864}{8} = \cancel{\frac{1572864}{8}} = 196608 \text{ bytes}$$ 6. **Convert bytes to kilobytes (KB):** $$\frac{196608}{1024} = \cancel{\frac{196608}{1024}} = 192 \text{ KB}$$ **Final answer:** The estimated file size is **192 KB**.