Question

Solve for x. Assume x is a 2 x 2 matrix.

a) x = [2 1; 3 4]
b) x = [0 -1; 2 5]
c) x = [1 0; 0 1]
d) x = [-1 2; 4 3]

Answer 1

To find the solution for x, we use the quadratic formula, substituting the coefficients a=1, b=0.0211, and c=-0.0211 into the formula. The two possible solutions for x are approximately 0.1351 and -0.1562.

Step-by-step explanation:

The question requires solving a quadratic equation for x. The provided equation is x² + 0.0211x - 0.0211 = 0. Using the quadratic formula, we can solve this equation. In this case, the coefficients are a = 1, b = 0.0211, and c = -0.0211. By substituting these into the quadratic formula, we get:

x = -b ± √(b² - 4ac) / 2a

Substituting the given values, we have:

x = -0.0211 ± √(0.0211² - 4 × 1 × -(0.0211)) / 2 × (1)

Which simplifies to:

x = -0.0211 ± √(0.000444 + 0.0844) / 2

x = -0.0211 ± √(0.084844) / 2

x = -0.0211 ± 0.29128 / 2

The two possible solutions for x are:

• x = (0.29128 - 0.0211) / 2
• x = -(0.29128 + 0.0211) / 2

Finally, the two solutions are:

• x ≈ 0.1351
• x ≈ -0.1562