Question

Solve the matrix equation ax = 0. If there is no solution, enter 'no solution'. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.

Answer 1

To solve the quadratic equation t² + 10t - 200 = 0, we use the quadratic formula, resulting in two solutions for t: 10 and -20.

Step-by-step explanation:

The question asks us to solve for t using the quadratic formula for the given equation t² + 10t - 200 = 0. To apply the quadratic formula, first confirm that the equation is in the standard form ax² + bx + c = 0, which it is. The quadratic formula is expressed as t = (-b ± √(b² - 4ac)) / (2a), where a = 1, b = 10, and c = -200.

To find the values of t, plug the coefficients into the formula: t = (-10 ± √((10)² - 4(1)(-200))) / (2(1)). Calculate the discriminant (the part under the square root), which is 10² - 4(1)(-200) = 100 + 800 = 900. Taking the square root of the discriminant, we get √900 = 30.

Now, solve for t using both the positive and negative square root: t = (-10 + 30) / 2 and t = (-10 - 30) / 2, resulting in t = 10 and t = -20, respectively. Thus, the equation has two solutions for t: 10 and -20.