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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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Let \(A\) be a square matrix. In the following, a sequence of matrices \(C_{j}\) converges if all of its elements converge.
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Let \(A\) be a square matrix. In the following, a sequence of matrices \(C_{j}\) converges if all of its elements converge.Let \(A\) be a square matrix. In the following, a sequence of matrices \(C_{j}\) converges if all of its elements converge. Prove that the following a ...
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asked in Mathematics 10 minutes ago
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Show that \(p(\lambda)=\lambda^{n}+a_{n-1} \lambda^{n-1}+\cdots+a_{0}\) is the characteristic polynomial of the matrix
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Show that \(p(\lambda)=\lambda^{n}+a_{n-1} \lambda^{n-1}+\cdots+a_{0}\) is the characteristic polynomial of the matrixShow that \(p(\lambda)=\lambda^{n}+a_{n-1} \lambda^{n-1}+\cdots+a_{0}\) is the characteristic polynomial of the matrix \ A=\left(\begin{array}{ccccc} ...
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asked in Mathematics 15 minutes ago
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The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ).
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The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ).The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ). a) If two square matrices ar ...
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asked in Mathematics 16 minutes ago
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Let \(C\) be a \(2 \times 2\) matrix of real numbers. Give a proof or counterexample to each of the following assertions:
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Let \(C\) be a \(2 \times 2\) matrix of real numbers. Give a proof or counterexample to each of the following assertions:Let \(C\) be a \(2 \times 2\) matrix of real numbers. Give a proof or counterexample to each of the following assertions: a) \(\operatorname{det}\left ...
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asked in Mathematics 40 minutes ago
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Let \(A\) be a square matrix. Proof or Counterexample. If \(A\) is diagonalizable, then so is \(A^{2}\).
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Let \(A\) be a square matrix. Proof or Counterexample. If \(A\) is diagonalizable, then so is \(A^{2}\).Let \(A\) be a square matrix. Proof or Counterexample. a) If \(A\) is diagonalizable, then so is \(A^{2}\). b) If \(A^{2}\) is diagonalizable, then so ...
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asked in Mathematics 44 minutes ago
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There are no square matrices \(A, B\) with the property that \(A B-B A=I .\) Proof or counterexample.
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There are no square matrices \(A, B\) with the property that \(A B-B A=I .\) Proof or counterexample.There are no square matrices \(A, B\) with the property that \(A B-B A=I .\) Proof or counterexample. REMARK: In quantum physics, the operators \(A u ...
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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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Let \(A\) and \(B\) be \(n \times n\) matrices with the property that \(A B=0 .\) For each of the following give a proof or counterexample.
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Let \(L\) be a \(2 \times 2\) matrix. For each of the following give a proof or counterexample.
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Let \(L\) be a \(2 \times 2\) matrix. For each of the following give a proof or counterexample.Let \(L\) be a \(2 \times 2\) matrix. For each of the following give a proof or counterexample. a) If \(L^{2}=0\) then \(L=0\). b) If \(L^{2}=L\) the ...
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asked in Mathematics 1 hour ago
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Let \(A, B\), and \(C\) be \(n \times n\) matrices.
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Let \(A, B\), and \(C\) be \(n \times n\) matrices.Let \(A, B\), and \(C\) be \(n \times n\) matrices. a) If \(A^{2}\) is invertible, show that \(A\) is invertible. NOTE: You cannot naively use the f ...
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asked in Mathematics 1 hour ago
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Let \(A\) be a real square matrix satisfying \(A^{17}=0\).
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Let \(A\) be a real square matrix satisfying \(A^{17}=0\).Let \(A\) be a real square matrix satisfying \(A^{17}=0\). a) Show that the matrix \(I-A\) is invertible. b) If \(B\) is an invertible matrix, is \(B ...
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asked in Mathematics 1 hour ago
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Let \(A\) be a square matrix with integer elements. For each of the following give a proof or counterexample.
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Let \(A\) be a square matrix with integer elements. For each of the following give a proof or counterexample.Let \(A\) be a square matrix with integer elements. For each of the following give a proof or counterexample. a) If \(\operatorname{det}(A)=\pm 1\), t ...
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asked in Mathematics 10 hours ago
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Let \(A\) and \(B\) be \(n \times n\) matrices with \(A B=0\). Give a proof or counterexample for each of the following.
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Let \(A\) and \(B\) be \(n \times n\) matrices with \(A B=0\). Give a proof or counterexample for each of the following.Let \(A\) and \(B\) be \(n \times n\) matrices with \(A B=0\). Give a proof or counterexample for each of the following.   a) Either \(A=0\) or ...
by MathsGee Platinum
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asked in Mathematics 10 hours ago
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What are the components of mathematical discourse?
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What are the components of mathematical discourse?What are the components of mathematical discourse? ...
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asked in Mathematics Jan 15
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What is mathematical discourse?
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What is mathematical discourse?What is mathematical discourse? ...
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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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Match the reasons to the lines of the following proof.
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Match the reasons to the lines of the following proof. Match the reasons to the lines of the following proof. Let $T$ be a triangle with vertices $u, v$, and $w$ in $\mathrm{C}$ where the vertices are n ...
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asked in Mathematics Jan 13
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You may choose the same option for matching more than once. Read through the following proof and match the lines with the reasons given below.
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You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines $L 1$ to $L 5$.

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