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arrow_back 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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in Mathematics
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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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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, Find a linear map of the plane, \(A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) that does the following transformation of the letter \(\mathbf{F}\) (here the smaller \(\mathbf{F}\) is transformed to the larger one):

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by MathsGee Platinum
(119,128 points)
asked in Mathematics Jan 13
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