Year 11 Maths - Methods Transformations

Using Matrices with Transformations

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Questions

Question 1

29097

A linear transformation is given as \(A = \left[ {\begin{array}{*{20}{c}}2&1\\{ - 1}&1\end{array}} \right]\), find the image of \(\left( { - 1,3} \right).\)

Answer

\(\left[ {\begin{array}{*{20}{c}}1\\4\end{array}} \right]\)

Worked Solution

\begin{align}
\begin{bmatrix}
x^{\prime} \\
y^{\prime}
\end{bmatrix} &=\begin{bmatrix}
2 & 1 \\
-1 & 1
\end{bmatrix}\begin{bmatrix}
-1 \\
3
\end{bmatrix} \\
&=\begin{bmatrix}
-2+3 \\
1+3
\end{bmatrix} \\
&=\begin{bmatrix}
1 \\
4
\end{bmatrix}
\end{align}

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