MHB Hint for a problem on condition number

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The discussion revolves around computing the condition number of a linear system defined by the equations 19x_1 + 20x_2 = b_1 and 20x_1 + 21x_2 = b_2. The condition number is calculated as 1601, derived from the norms of the coefficient matrix and its inverse, both yielding a norm of 41. The participants debate whether introducing a perturbation variable for the right-hand side constants is necessary to assess the system's sensitivity to changes in b_1 and b_2. They also discuss the method used for computing the matrix norm, with one participant confirming the use of a specific norm definition. The conversation concludes with a focus on whether the computed condition number sufficiently addresses the problem's requirements.
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I would like to know if the second part of this question is asking something different.

**Problem:** Consider the linear system $19x_1+20x_2=b_1, 20x_1+21x_2=b_2$. Compute the condition number of the coefficient matrix. Is the system well-conditioned with respect to perturbations of the right-handside constants ${b_1,b_2}$?

Do I need to introduce a $\delta$ into the right-handside, or is computing the coefficient number enough to conjecture about the condition of the right-handside constants?

Thanks.
 
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The second part of the problem as asking if the condition number you just computed is highly dependent on $b_{1}$ and $b_{2}$. What happens if you change the RHS's just a little? Does the condition number change a lot when you do that? I don't think you need to introduce another variable, at least not yet. What do you get for the condition number? And how are you computing it?
 
I get 1601 = 41*41 for the condition number, and I got it by computing the norm of the matrix A and the norm of the matrix A^(-1), an then multiplying them together. The norms of the matrices are both 41.

Isn't this enough for the purposes of this problem?
 
Did you use the formula
$$\|A\|= \max \{ \|Ax \|:x \in \mathbb{R}^{2}, \|x \|=1 \}?$$
If so, what vector norm did you use? Euclidean?
 
I used the following norm:

$$\|A_{n\mathbb x n}|=\max_{1\leq i \leq n}\sum_{j=1}^{n}\|a_{ij}\|$$
 
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