Test I
... 6. (15 pts.) Given the matrix B below, use any method to evaluate det(B). From your answer, determine whether B has an inverse. If it does, use Cramer’s rule to find the (3,1)-entry the inverse. ...
... 6. (15 pts.) Given the matrix B below, use any method to evaluate det(B). From your answer, determine whether B has an inverse. If it does, use Cramer’s rule to find the (3,1)-entry the inverse. ...
1 Residual life for gamma and Weibull distributions
... where C denotes a generic constant which does not depend on θ or x. The corresponding inequalities for the rc, lc, and nc cases are obtained in precisely the same way, and, using Cauchy’s inequality, it follows that |mθ1 (x) − mθ2 (x))| ≤ Ckθ1 − θ2 k, with k · k denoting Euclidean norm, so that the ...
... where C denotes a generic constant which does not depend on θ or x. The corresponding inequalities for the rc, lc, and nc cases are obtained in precisely the same way, and, using Cauchy’s inequality, it follows that |mθ1 (x) − mθ2 (x))| ≤ Ckθ1 − θ2 k, with k · k denoting Euclidean norm, so that the ...
Solutions to HW 5
... Proof. We first prove the “only if” implication. So assume that T : V → W is an isomorphism; we first claim that then T(β) must be a linearly independent set of n vectors in W . To that end, write β = {v1 , . . . , vn }. Because T is one-to-one, the vectors T(vk ) are distinct for 1 ≤ k ≤ n, and thu ...
... Proof. We first prove the “only if” implication. So assume that T : V → W is an isomorphism; we first claim that then T(β) must be a linearly independent set of n vectors in W . To that end, write β = {v1 , . . . , vn }. Because T is one-to-one, the vectors T(vk ) are distinct for 1 ≤ k ≤ n, and thu ...
