Pearson Edexcel IAL Mathematics FP3.6.6 Inverse transformations & combinations

Practise reversing matrix transformations and combinations to recover original points, vectors or lines from their transformed forms.

Exam points

apply an inverse matrix to a transformed vector equation to recover the original line
use the inverse of a combined transformation when working backwards from an image

[Maximum number: 4]

\mathbf{A}=\left(\begin{array}{rrr} 1 & -1 & 1 \\ 1 & 1 & 1 \\ 1 & 2 & a \end{array}\right) \quad a \neq 1

Find a vector equation for the line $l_{1}$

$a=4,\quad A^{-1}=\frac16((2,6,-2),(-3,3,0),(1,-3,2))$

B1ft

$\frac16((2,6,-2),(-3,3,0),(1,-3,2))(12-6\lambda,\ 4+2\lambda,\ 6+3\lambda)^T$

M1

$=(6-\lambda,\ -4+4\lambda,\ 2-\lambda)^T$

A1

$\mathbf r=(6,-4,2)^T+\lambda(-1,4,-1)^T$

A1

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FP3.6.6 - Inverse transformations and combinations question 1