Year 11 Maths - Methods Transformations

Matrices

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Questions

Question 1

29085

Let \(X = \left[ \begin{array}{l} - 1\\{\rm{ }}2\end{array} \right]\) and \(Y = \left[ \begin{array}{l}2\\0\end{array} \right]\), find \(2X - Y.\)

Answer

\(\left[ \begin{array}{c} - 4\\{\rm{ }}4\end{array} \right]\)

Worked Solution

\begin{align}
&2X=2\begin{bmatrix}
-1 \\
2
\end{bmatrix}=\begin{bmatrix}
-2 \\
4
\end{bmatrix}\\
&2 X-Y=\begin{bmatrix}
-2 \\
4
\end{bmatrix}-\begin{bmatrix}
2 \\
0
\end{bmatrix}=\begin{bmatrix}
-2-2 \\
4-0
\end{bmatrix}=\begin{bmatrix}
-4 \\
4
\end{bmatrix}
\end{align}

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