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In: Advanced Math

For a 2 by 2 invertible matrix A, define the condition number to be cond(A) =...

For a 2 by 2 invertible matrix A, define the condition number to be cond(A) = ||A|| ⋅ ||A||-1. Assume that the matrix norm is defined using the Euclidean vector norm.

(a) Find two 2by2 invertible matrices B and C such that cond(B + C) < cond(B) + cond(C).

(b) Find two 2by2 invertible matrices B and C such that cond(B + C) > cond(B) + cond(C).

(c) Suppose that A is a symmetric invertible 2by2 matrix. Find cond(2A) and cond(A2) in terms of cond(A).

(d)do the results from part (c) hold if A is not symmetric? You can either prove the results, or find counterexamples.

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Expert Solution

Colby Messinger answered 2 years ago
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