Determine the matrix representation of each of the following composite transformations. A pitch of 90^(circ) followed by a yaw of 90^(circ)

Determine the matrix representation of each of the following composite transformations. A pitch of ${90}^{\circ }$ followed by a yaw of ${90}^{\circ }$

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Theodore Schwartz

If L is pitch transformation with the angle of theta, the matrix representation of L is given by,
$p=\left[\left(\mathrm{cos}\theta ,\mathrm{sin}\theta ,o\right),\left(-\mathrm{sin}\theta ,\mathrm{cos}\theta ,0\right),\left(0,0,1\right)\right]$
If L is the pitch transformation with the angle of rotation phi, the matrix representation of L is given by
$\left[\left(\mathrm{cos}\varphi ,0,-\mathrm{sin}\varphi \right),\left(0,1,0\right),\left(\mathrm{sin}\varphi ,0,\mathrm{cos}\varphi \right)\right]$
$py=\left[\left(\left(\mathrm{cos}{90}^{\circ }\right),\left(\mathrm{sin}{90}^{\circ }\right),0\right),\left(\left(-\mathrm{sin}{90}^{\circ }\right),\left(\mathrm{cos}{90}^{\circ }\right),0\right),\left(0,0,1\right)\right]\left[\left(\left(\mathrm{cos}{90}^{\circ }\right),0,\left(-\mathrm{sin}{90}^{\circ }\right)\right),\left(0,1,0\right),\left(\left(\mathrm{sin}90v\right),0,\left(\mathrm{cos}{90}^{\circ }\right)\right)\right]$
$=\left[\left(0,1,0\right),\left(-1,0,0\right),\left(0,0,1\right)\right]\left[\left(0,0,-1\right),\left(0,1,0\right),\left(1,0,0\right)\right]$
$=\left[\left(0,1,0\right),\left(0,0,1\right),\left(1,0,0\right)\right]$

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