3.
$$\mathbf { A } = \left( \begin{array} { c c c }
1 & 0 & 0
0 & \frac { \sqrt { 3 } } { 2 } & - \frac { 1 } { 2 }
0 & \frac { 1 } { 2 } & \frac { \sqrt { 3 } } { 2 }
\end{array} \right)$$
- Describe fully the single geometric transformation \(A\) represented by the matrix \(\mathbf { A }\).
$$\mathbf { B } = \left( \begin{array} { c c c }
1 & 3 & 0
\sqrt { 3 } & 0 & 5 \sqrt { 3 }
1 & 2 & 0
\end{array} \right)$$
The transformation \(B\) is represented by the matrix \(\mathbf { B }\).
The transformation \(A\) followed by the transformation \(B\) is the transformation \(C\), which is represented by the matrix \(\mathbf { C }\).
To determine matrix \(\mathbf { C }\), a student attempts the following matrix multiplication.
$$\left( \begin{array} { c c c }
1 & 0 & 0
0 & \frac { \sqrt { 3 } } { 2 } & - \frac { 1 } { 2 }
0 & \frac { 1 } { 2 } & \frac { \sqrt { 3 } } { 2 }
\end{array} \right) \left( \begin{array} { c c c }
1 & 3 & 0
\sqrt { 3 } & 0 & 5 \sqrt { 3 }
1 & 2 & 0
\end{array} \right)$$ - State the error made by the student.
- Determine the correct matrix \(\mathbf { C }\).