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Compute the value of the determinant of the \(3 \times 3\) complex matrix \(X\), provided that...
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Compute the value of the determinant of the \(3 \times 3\) complex matrix \(X\), provided that...Compute the value of the determinant of the \(3 \times 3\) complex matrix \(X\), provided that \(\operatorname{tr}(X)=1, \operatorname{tr}\left(X^{2}\ ...
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asked in Mathematics 8 minutes ago
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Let \(A\) be a \(3 \times 3\) matrix with eigenvalues \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) ...
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Let \(A\) be a \(3 \times 3\) matrix with eigenvalues \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) ...Let \(A\) be a \(3 \times 3\) matrix with eigenvalues \(\lambda_{1}, \lambda_{2}, \lambda_{3}\) and corresponding linearly independent eigenvectors \( ...
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Suppose that \(A\) is a \(3 \times 3\) matrix with eigenvalues \(\lambda_{1}=-1, \lambda_{2}=0\) and \(\lambda_{3}=1\), and corresponding eigenvectors

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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 ...
by MathsGee Platinum
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asked in Mathematics 37 minutes ago
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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 ...
by MathsGee Platinum
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asked in Mathematics 1 hour ago
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Find a real \(2 \times 2\) matrix \(A\) (other than \(A=I\) ) such that \(A^{5}=I\).
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Find a matrix that rotates the plane through \(+60\) degrees, keeping the origin fixed.
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Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees followed by a reflection across the horizontal axis.
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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 ...
by MathsGee Platinum
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asked in Mathematics 9 hours ago
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Let \(A\) be a \(4 \times 4\) matrix with determinant 7 . Give a proof or counterexample for each of the following.
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Let \(A\) be a \(4 \times 4\) matrix with determinant 7 . Give a proof or counterexample for each of the following.Let \(A\) be a \(4 \times 4\) matrix with determinant 7 . Give a proof or counterexample for each of the following.   a) For some vector \(\mat ...
by MathsGee Platinum
(104,076 points)
asked in Mathematics 10 hours ago
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Let \(U\) and \(V\) both be two-dimensional subspaces of \(\mathbb{R}^{5}\), and let \(W=U \cap V\). Find all possible values for the dimension of \(W\).
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Which of the following sets are linear spaces?
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Which of the following sets are linear spaces?Which of the following sets are linear spaces? a) \(\left\{X=\left(x_{1}, x_{2}, x_{3}\right)\right.\) in \(\mathbb{R}^{3}\) with the property \(\lef ...
by MathsGee Platinum
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asked in Mathematics 14 hours ago
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At noon the minute and hour hands of a clock coincide.
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At noon the minute and hour hands of a clock coincide.At noon the minute and hour hands of a clock coincide. a) What in the first time, \(T_{1}\), when they are perpendicular? b) What is the next time, \ ...
by MathsGee Platinum
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asked in Mathematics 14 hours ago
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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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Determine \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) if \[ y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2} \]
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Calculate \(h^{\prime}(y)\) for: \[ h(y)=-8 y^{3}-7 y^{2}+y^{1,5}+3 y^{0,8} \]
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Differentiate \(k(t)=\frac{(t+2)^{3}}{\sqrt{t}}\) with respect to \(t\)
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Differentiate \(g(t)=4(t+1)^{2}(t-3)\) with respect to \(t\)
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Differentiate the function \(y=3 x^{5}\)
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In mathematics/algebra, what is the difference between \(|x|\) and \(||x||\)?
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