Final answer:
A matrix is invertible if its determinant is nonzero. For a quadratic equation ax² + bx + c = 0, the matrix will be invertible when the determinant, calculated as b² - 4ac, is greater than zero. The constants provided, a = 1.00, b = 10.0, and c = -200, don't directly answer the invertibility without context, but the determinant (b² - 4ac) indicates the conditions for invertibility.
Step-by-step explanation:
The student's question is asking for the conditions under which a matrix a will be invertible. A matrix is invertible if its determinant is not zero. Specifically, if a matrix is represented by a quadratic equation ax² + bx + c = 0, it will be invertible when the determinant (b² - 4ac) is greater than zero. To find the invertible values of c, we solve for c when the determinant is positive.
Using the quadratic formula, we can express the solutions for a quadratic equation. However, the actual calculation of whether a is invertible isn't given here since only the constants a, b, and c are provided without mentioning they are part of a matrix. In a different context, finding the side of a right triangle with sides a, b, and hypotenuse c involves calculating the square root of (c² - b²) to 'invert' a² to find a. This is not directly related to the concept of a matrix being invertible but shows a method of 'inverting' an operation.