(b) State (without proof) the Kolmogorov zero-one law.
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- 1 2 5 - 2 Let A = = A- [ ' ₂₁² ]· •, - - ² - ₂ -[ 0 ]-D₂- [ - ²6 ] · G] b3 5 12 19 16 a. Find A X = and b4 +-[42] 12 1 and use it solve the four equations Ax=b₁, Ax=b₂,Ax=b3, and Ax=b4. b. The four equations in part (a) can be solved by the same set of operations, since the coefficient matrix is the same in each case. Solve the four equations in part (a) by row reducing the augmented matrix [A b₁ b₂ b3 b4]. .... 12 -4 (Type an integer or simplified fraction for each matrix element.) b. Solve the four equations by row reducing the augmented matrix [A b₁ b₂ b3 b4]. Write the augmented matrix [A b₁ b₂ b3 b4] in reduced echelon form.1.5.1. (a) Show, that if x₁ and 2 are two solutions of a quadratic equation ax² + bx + c = 0 (with b с a 0), then x1 + x2 = −; and x₁ x2 = (these are often called Vieta's Formulas). Also, find a a a formula for x² + x² in terms of a, b and c. (b) Use Part (a) to find a quadratic equation with two distinct real solutions, given that the sum of the solutions is 47 and their product -59.