MHB Solving a Matrix Problem on IGCSE Past Paper: Part B

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The discussion focuses on solving a matrix problem from an IGCSE past paper, specifically part B, which involves finding the value of t in the equation $[M]^{-1} \cdot [M] = [I]$. Participants suggest multiplying the given matrices and equating the resulting elements to those in the identity matrix. This approach will help derive an equation in terms of t. The discussion encourages trying out the multiplication and setting up the equations to find the solution. Engaging with this method is essential for mastering matrix concepts in preparation for the IGCSE exam.
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I have been teaching myself matrices for my IGCSE course and I ran into a problem in a past paper which I have no clue how to solve. The problem is part b of the attached image. Thanks for your help in advance.View attachment 9518
 

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$[M]^{-1} \cdot [M] = $

$\begin{bmatrix}
-5t & 6\\
t & -t
\end{bmatrix}
\cdot
\begin{bmatrix}
t & 6\\
t & 5t
\end{bmatrix}=
\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$

Multiply $[M]^{-1} \cdot [M]$ , then set each corresponding element in the product equal to the elements in the identity matrix to get the desired equation in $t$.

Give it a go and see how you do ...
 
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