# Recent questions tagged equation

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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...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}\ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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 $\lambda_{1}, \lambda_{2}, \lambda_{3}$ ...Let $A$ be a $3 \times 3$ matrix with eigenvalues $\lambda_{1}, \lambda_{2}, \lambda_{3}$ and corresponding linearly independent eigenvectors $... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Suppose that \(A$ is a $3 \times 3$ matrix with eigenvalues $\lambda_{1}=-1, \lambda_{2}=0$ and $\lambda_{3}=1$, and corresponding eigenvectors
Suppose that $A$ is a $3 \times 3$ matrix with eigenvalues $\lambda_{1}=-1, \lambda_{2}=0$ and $\lambda_{3}=1$, and corresponding eigenvectorsSuppose 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:
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 ... close 0 answers 4 views Let \(A$ be an $m \times n$ matrix, and suppose $\vec{v}$ and $\vec{w}$ are orthogonal eigenvectors of $A^{T} A$. Show that $A \vec{v}$ and $A \vec{w}$ are orthogonal.Let $A$ be an $m \times n$ matrix, and suppose $\vec{v}$ and $\vec{w}$ are orthogonal eigenvectors of $A^{T} A$. Show that $A \vec{v}$ and ...
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Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \vec{v}=\vec{w}$ and $R \vec{w}=\vec{v}$.Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \v ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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.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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Linear maps $F(X)=A X$, where $A$ is a matrix, have the property that $F(0)=A 0=0$, so they necessarily leave the origin fixed. It is simple to extend this to include a translation, Linear maps $F(X)=A X$, where $A$ is a matrix, have the property that $F(0)=A 0=0$, so they necessarily leave the origin fixed. It is simple t ...
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Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$.
Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$.Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$. ...
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Find a $3 \times 3$ matrix $A$ mapping $\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ that rotates the $x_{1} x_{3}$ plane by 60 degrees and leaves the $x_{2}$ axis fixed.Find a $3 \times 3$ matrix $A$ mapping $\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ that rotates the $x_{1} x_{3}$ plane by 60 degrees and leav ...
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Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 degrees.
Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 degrees.Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 ...
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Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.
Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.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.
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis.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.
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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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.Let $A$ be a $4 \times 4$ matrix with determinant 7 . Give a proof or counterexample for each of the following. &nbsp; a) For some vector $\mat ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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 $W$.
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 $W$.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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following sets are linear spaces? 0 answers 6 views 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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 At noon the minute and hour hands of a clock coincide. 0 answers 5 views 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, \ ...
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What is affirming the consequent?
What is affirming the consequent?What is affirming the consequent? ...
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Determine $\frac{\mathrm{d} y}{\mathrm{~d} x}$ if $y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2}$
Determine $\frac{\mathrm{d} y}{\mathrm{~d} x}$ if $y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2}$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: $h(y)=-8 y^{3}-7 y^{2}+y^{1,5}+3 y^{0,8}$
Calculate $h^{\prime}(y)$ for: $h(y)=-8 y^{3}-7 y^{2}+y^{1,5}+3 y^{0,8}$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 $t$
Differentiate $k(t)=\frac{(t+2)^{3}}{\sqrt{t}}$ with respect to $t$Differentiate $k(t)=\dfrac{(t+2)^{3}}{\sqrt{t}}$ with respect to $t$ ...
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Differentiate $g(t)=4(t+1)^{2}(t-3)$ with respect to $t$
Differentiate $g(t)=4(t+1)^{2}(t-3)$ with respect to $t$Differentiate &nbsp;$g(t)=4(t+1)^{2}(t-3)$ with respect to $t$ ...
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Differentiate the function $y=3 x^{5}$
Differentiate the function $y=3 x^{5}$Differentiate the function $y=3 x^{5}$ ...
In mathematics/algebra, what is the difference between $|x|$ and $||x||$?
In mathematics/algebra, what is the difference between $|x|$ and $||x||$?In mathematics/algebra, what is the difference between $|x|$ and $||x||$? ...