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Recent questions tagged prove


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Let \(A\) be a square matrix and let \(\|B\|\) be any norm on matrices [one example is \(\left.\|B\|=\max _{i, j}\left|b_{i j}\right|\right]\).
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Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).
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Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).Let \(A, B\), and \(C\) be any \(n \times n\) matrices. a) Show that \(\operatorname{trace}(A B)=\operatorname{trace}(B A)\). b) Show that \(\operator ...
by MathsGee Platinum
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asked in Mathematics 1 hour ago
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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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Answer the following in terms of \(\mathbf{V}, \mathbf{W}\), and \(\mathbf{Z}\).
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Answer the following in terms of \(\mathbf{V}, \mathbf{W}\), and \(\mathbf{Z}\).Let \(A\) be a matrix, not necessarily square. Say \(\mathbf{V}\) and \(\mathbf{W}\) are particular solutions of the equations \(A \mathbf{V}=\mathbf{ ...
by MathsGee Platinum
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asked in Mathematics 1 hour ago
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent.
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent.Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent. a) For every \(y \in \mathbb{R}^{k}\) th ...
by MathsGee Platinum
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asked in Mathematics 14 hours ago
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What is aleph?
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What is aleph?What is aleph? ...
by Pieter SIlver Status
(18,309 points)
asked in Mathematics Jan 15
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What is affirming the consequent?
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What is affirming the consequent?What is affirming the consequent? ...
by Pieter SIlver Status
(18,309 points)
asked in Mathematics Jan 15
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Show that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfy
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If $\mathbf{v}$ is a vector in $R^{n}$, and if $k$ is any scalar, then prove that $\|k \mathbf{v}\|=|k|\|\mathbf{v}\|$
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Prove the orthogonal projection theorem
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Prove the orthogonal projection theoremProve the orthogonal projection theorem ...
by MathsGee Platinum
(104,076 points)
asked in Mathematics Jan 13
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