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Proof or counterexample. In these \(L\) is a linear map from \(\mathbb{R}^{2}\) to \(\mathbb{R}^{2}\), so its representation will be as a \(2 \times 2\) matrix.

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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 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 \(A^{5}=I\). ...
by MathsGee Platinum
(103,816 points)
asked in Mathematics 35 minutes ago
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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.

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Find the inverse to a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).
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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 reflects across the horizontal axis followed by a rotation the plane by \(+45\) degrees.
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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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Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).
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Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise). ...
by MathsGee Platinum
(103,816 points)
asked in Mathematics 41 minutes ago
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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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How do I determine the equation of a normal in $R^2$ or $R^3$?
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How do I determine the equation of a normal in $R^2$ or $R^3$?How do I determine the equation of a normal in $R^2$ or $R^3$? ...
by MathsGee Platinum
(103,816 points)
asked in Mathematics Jan 13
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What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
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Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is
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Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.
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Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.
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A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?

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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to
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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal toThe distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to   A) $\dfrac{1}{3}$ B) 3 C) $\dfrac{1}{15}$ D) 5 E) no ...
by MathsGee Platinum
(103,816 points)
asked in Mathematics Jan 13
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Determine whether planes $2 x+y+z-1=0,-x+3 y-2 z-3=0$ and $3 x-y=-1$ intersect. If yes, find the intersection.
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Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$.
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Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$
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Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$ \begin{equation} \text { A. }\left|\begin{array} ...
by MathsGee Platinum
(103,816 points)
asked in Mathematics Jan 13
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Which of the following is the equation of the plane which passes through the point $A(-3,4,-3)$ and contains the line $v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$

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Which of the following is the unit vector in direction of $a \times b$ if $a=(2,1,1)$ and $b=(-1,2,2) ?$
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Which of the following is the unit vector in direction of $a \times b$ if $a=(2,1,1)$ and $b=(-1,2,2) ?$Which of the following is the unit vector in direction of $a \times b$ if $a=(2,1,1)$ and $b=(-1,2,2) ?$   A. $\left(-\frac{1}{2}, \frac{1}{2}, ...
by MathsGee Platinum
(103,816 points)
asked in Mathematics Jan 13
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