A 256 x 256 matrix requires how much more computer memory than a 64 x 64 matrix?

To determine how much more computer memory a 256 x 256 matrix requires compared to a 64 x 64 matrix, it's essential to calculate the number of elements in each matrix, as each element typically requires the same amount of storage.

The memory required by a matrix is proportional to the number of its elements. A 64 x 64 matrix contains 64 multiplied by 64, which equals 4,096 elements. A 256 x 256 matrix contains 256 multiplied by 256, which equals 65,536 elements.

To find the ratio of the memory requirements, divide the number of elements in the larger matrix by the number of elements in the smaller matrix:

65,536 (elements in the 256 x 256 matrix) ÷ 4,096 (elements in the 64 x 64 matrix) = 16.

This indicates that the 256 x 256 matrix requires 16 times more memory than the 64 x 64 matrix. Given this understanding, the choice stating that it requires 4 times more memory is not accurate because the ratio is significantly higher at 16 times the memory requirement.

Thus, the correct conclusion is that the larger matrix requires a total of 16 times more memory than