\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Courses
About
Login
Register
C
⌫
\(\pi\)
e
\(\frac{a}{b}\)
!
←
→
(
)
\(\sqrt{\,}\)
\(a^{b}\)
7
8
9
\(\div\)
log
ln
4
5
6
\(\times\)
cos
cos⁻¹
1
2
3
-
sin
sin⁻¹
0
.
=
+
tan
tan⁻¹
Consider two transformations:
\(T_1\): A shear parallel to the x-axis that maps \((1,0)\) to \((1,0)\) and \((0,1)\) to \((2,1)\).
\(T_2\): A rotation of \(90^\circ\) anti-clockwise about the origin.
Find the matrix \(\mathbf{A}\) representing \(T_1\).
Find the matrix \(\mathbf{B}\) representing \(T_2\).
Find the matrix \(\mathbf{C}\) representing the composite transformation \(T_1\) followed by \(T_2\).
Find the image of the point \(P(1, 1)\) under this composite transformation.
Find the coordinates of point \(S\) such that its image under this composite transformation is \(S'(-1, 5)\).
(You are given that \(\mathbf{C}^{-1} = \begin{pmatrix} 2 & 1 \\ -1 & 0 \end{pmatrix}\)).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.
Exit