# Recent questions tagged trace

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Why should levels of carbon and greenhouse gases in the atmosphere be reduced?
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How can businesses leverage customer trace data?
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What is customer trace data and why is it valuable?
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What is the rank of a matrix?
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One writes 268 numbers around a circle such that the sum of 20 consecutive numbers is always equal to 75 . The numbers 3,4 and 9 are written in positions 17,83 and 144 re...
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30 numbers $$a_{1}, \ldots, a_{30}$$ are written along the circle in such a way that each of them is equal to the absolute value of the difference between the next two in...
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If carbon dioxide is a trace gas in our atmosphere, why does it matter?
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Let $$A=\left(a_{i j}\right)$$ be an $$n \times n$$ matrix with the property that its absolute row sums are at most 1 , that is, $$\left|a_{i 1}\right|+\cdots+\left|a_{\t... 493 views 0 answers Let \(A$$ be a square matrix and let $$\|B\|$$ be any norm on matrices [one example is $$\left.\|B\|=\max _{i, j}\left|b_{i j}\right|\right]$$. To what extent are the con...
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Let $$\alpha_{1}, \ldots, \alpha_{n}$$ be positive real numbers and let $$A=\left(a_{i j}\right)$$ where $$a_{i j}=\alpha_{i} / \alpha_{j} .$$ Say as much as you can abou...
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Every real upper triangular $$n \times n$$ matrix $$\left(a_{i j}\right)$$ with $$a_{i i}=1, i=1,2, \ldots, n$$ is invertible. Proof or counterexample.
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Let $$A$$ be the rank one $$n \times n$$ matrix $$A=\left(v_{i} v_{j}\right)$$, where $$\vec{v}:=\left(v_{1}, \ldots, v_{n}\right)$$ is a non-zero real vector.a) Find its...
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Let $$A=\left(a_{i j}\right)$$ be an $$n \times n$$ matrix whose rank is 1 . Let $$v:=\left(v_{1}, \ldots, v_{n}\right) \neq 0$$ be a basis for the image of $$A$$.a) Show...