Challenging +1.2 This is a Further Maths question requiring students to decompose a composite transformation into two shear matrices and solve a matrix equation. While it involves matrix multiplication and algebraic manipulation, the approach is methodical: writing shears in standard form, multiplying them, equating coefficients to the given matrix, and solving the resulting system. The 7 marks suggest extended working, but the technique is standard for FM students who have studied transformations.
A transformation is equivalent to a shear parallel to the x-axis followed by a shear parallel to the y-axis and is represented by the matrix \(\begin{pmatrix} 1 & s \\ t & 0 \end{pmatrix}\).
Find in terms of s the matrices which represent each of the shears. [7]
A transformation is equivalent to a shear parallel to the x-axis followed by a shear parallel to the y-axis and is represented by the matrix $\begin{pmatrix} 1 & s \\ t & 0 \end{pmatrix}$.
Find in terms of s the matrices which represent each of the shears. [7]
\hfill \mbox{\textit{SPS SPS FM 2023 Q10 [7]}}