AI HL · AHL 5
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Definition and arithmetic of matrices
AHL 5.1
Template key, then the matrix template · name it with :=
Screenshot and video to come
State the order of \(\begin{pmatrix}4 & 0 & -1 \\ 2 & 7 & 3\end{pmatrix}\).
Have a go first. Then open the working one line at a time.
2 rows, 3 columns
Rows go across. Columns go down.
2 × 3
Rows first. It is not 6: the order is a label.
Given that \(\begin{pmatrix}2x-1 & 4 \\ 3 & x+y\end{pmatrix} = \begin{pmatrix}9 & 4 \\ 3 & 2\end{pmatrix}\), find \(x\) and \(y\).
Have a go first. Then open the working one line at a time.
\(2x - 1 = 9\), so \(x = 5\)
Matching elements are equal.
\(x + y = 2\), so \(y = -3\)
Use \(x = 5\).
\(A = \begin{pmatrix}4 & -2 \\ 1 & 6 \\ -3 & 0\end{pmatrix}\) and \(B = \begin{pmatrix}-1 & 5 \\ 2 & -4 \\ 7 & 3\end{pmatrix}\). Find \(A - B\).
Have a go first. Then open the working one line at a time.
Both are 3 × 2
So they can be subtracted.
\(A - B = \begin{pmatrix}4-(-1) & -2-5 \\ 1-2 & 6-(-4) \\ -3-7 & 0-3\end{pmatrix}\)
Take care subtracting a negative.
\(\begin{pmatrix}5 & -7 \\ -1 & 10 \\ -10 & -3\end{pmatrix}\)
On the calculator: a − b.
A gym's monthly income, in euros, from adult and student members at its two sites is \(\begin{pmatrix}2400 & 1500 \\ 1800 & 2100\end{pmatrix}\). Income is expected to rise by 5% everywhere. Find the matrix of expected income.
Have a go first. Then open the working one line at a time.
\(1.05\)
A 5% rise multiplies by 1.05.
\(1.05\begin{pmatrix}2400 & 1500 \\ 1800 & 2100\end{pmatrix} = \begin{pmatrix}2520 & 1575 \\ 1890 & 2205\end{pmatrix}\)
Every element changes by the same factor.
\(A = \begin{pmatrix}3 & -1 \\ 0 & 4\end{pmatrix}\) and \(B = \begin{pmatrix}1 & 2 \\ -2 & 5\end{pmatrix}\). Find \(2A - 3B\).
Have a go first. Then open the working one line at a time.
\(2A = \begin{pmatrix}6 & -2 \\ 0 & 8\end{pmatrix},\quad 3B = \begin{pmatrix}3 & 6 \\ -6 & 15\end{pmatrix}\)
Scalars first.
\(2A - 3B = \begin{pmatrix}3 & -8 \\ 6 & -7\end{pmatrix}\)
\(0 - (-6) = 6\).