Specialist Mathematics · Unit 2 · Matrices and transformations · Transformations in the plane
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A linear transformation T is defined by the matrix T = $\begin{pmatrix} 4 & 3 \\ -2 & 1 \end{pmatrix}\u0024. (a) Determine the inverse matrix T⁻¹. Show evidence of your calculation. (b) Verify that T × T⁻¹ = I, where I is the identity matrix.
A linear transformation \[T: \mathbb{R}^2 \to \mathbb{R}^2\] is represented by the matrix \[A = \begin{pmatrix} 3 & 1 \\ 2 & 1 \end{pmatrix}.\] a) Determine the inverse matrix \[A^{-1}\] by finding the determinant and using the inverse formula. Show all working. b) Hence verify that \[A \cdot A^{-1} = I\] where \[I\] is the identity matrix.
Which of the following matrices is the inverse of \( M = \begin{pmatrix} 3 & 1 \\ 2 & 1 \end{pmatrix} \)?
A linear transformation \(T: \mathbb{R}^2 \to \mathbb{R}^2\) is represented by the matrix \(M = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\). The diagram shows the image of the unit square \(OABC\) under this transformation. Determine the matrix representing the inverse transformation \(T^{-1}\).