1. The problem asks to calculate the estimated file size for a 512x512 matrix with a bit depth of 6. 2. The formula to calculate file size in bits is: $$\text{File size (bits)} = \text{width} \times \text{height} \times \text{bit depth}$$ 3. To convert bits to bytes, divide by 8 since 1 byte = 8 bits: $$\text{File size (bytes)} = \frac{\text{File size (bits)}}{8}$$ 4. Substitute the values: $$\text{File size (bits)} = 512 \times 512 \times 6 = 1572864$$ 5. Convert bits to bytes: $$\text{File size (bytes)} = \frac{1572864}{8} = \cancel{\frac{1572864}{8}}196608$$ 6. So, the estimated file size is 196608 bytes. This means the file will take approximately 196608 bytes of storage space.