Let's find the condition number for a simple 1x1 'matrix' (just a number) to understand the idea.

Step 1: Consider a very simple 'system' like finding 'x' in the equation 2x = 6. Here, our 'matrix' is just the number 2.
---Step 2: The condition number for a single number 'a' is usually considered to be 1, because its inverse is 1/a. The ratio of its magnitude to its inverse's magnitude is not really useful here. Let's use a slightly more complex example with a 2x2 matrix concept for illustration, even if we simplify the calculation.
---Step 3: For a general matrix A, the condition number (often using the '2-norm' or 'Frobenius norm') is roughly 'norm(A) * norm(inverse(A))'. The 'norm' is like a size or magnitude.
---Step 4: Imagine a matrix A = [[10, 1], [1, 0.1]]. This matrix is 'nearly singular' because the second row is almost a multiple of the first.
---Step 5: The inverse of A, A^-1, would be approximately [[-0.5, 5], [5, -50]]. (Calculating exact inverse for 2x2 is (1/det(A)) * adj(A)). Here, det(A) = (10*0.1) - (1*1) = 1 - 1 = 0. This means this matrix is actually singular, and its inverse does not exist. A singular matrix has an infinite condition number.
---Step 6: Let's take a slightly different matrix to avoid singularity: A = [[10, 1], [1, 0.2]].
---Step 7: Determinant = (10*0.2) - (1*1) = 2 - 1 = 1. Inverse A^-1 = [[0.2, -1], [-1, 10]].
---Step 8: If we approximate 'norm(A)' as the maximum absolute value in A (which is 10) and 'norm(A^-1)' as the maximum absolute value in A^-1 (which is 10), then the condition number is roughly 10 * 10 = 100. This is a high number, meaning small changes in A could lead to large changes in the solution. This illustrates the concept, though actual norm calculations are more involved.
Answer: A high condition number (like 100 in our simplified example) indicates that the problem is sensitive to small changes in input.