Edexcel IAL Mathematics FP3 Combination of Transformations

Practise Edexcel IAL Mathematics FP3 transformation combinations by forming matrix equations and solving constants from TU equals I.

Exam points

Use a matrix product such as TU = I to form simultaneous equations in unknown constants.
Solve for constants a, b and c from the matrix entries and show enough equations for method marks.

[Maximum number: 4]

\mathbf{T}=\left(\begin{array}{lll} 2 & 3 & 7 \\ 3 & 2 & 6 \\ a & 4 & b \end{array}\right) \quad \mathbf{U}=\left(\begin{array}{rrr} 6 & -1 & -4 \\ 15 & c & -9 \\ -8 & a & 5 \end{array}\right)

where a, b and c are constants.
Given that T U=I

determine the value of a, the value of b and the value of c

\mathbf{TU}=\mathbf I

6a+60-8b=0,\quad -4a-36+5b=1

6a-8b=-60,\quad -4a+5b=37

a=2,\quad b=9

-2+3c+7a=0

c=-4

M1: obtains at least two equations with at least one correct.\ndM1: obtains values for two of a,b,c.\nA1 A1: a=2,b=9,c=-4.

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