Study Mathematics worksheet on Matrices for Secondary. Useful for revision, homework, and exam preparation in Zimbabwe.
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This is the Mathematics worksheet. It is a free worksheet for revision.
Finding the values of the unknomer
- The corresponding numbers or lettes have the fame value.
\[
\begin{array}{l}
\text { e.g }\left[\begin{array}{l}
x
y
\end{array}\right]=\left[\begin{array}{l}
2
3
\end{array}\right]
\therefore \underset{\left[\begin{array}{ll}
a | b
c | d
\end{array}\right]=\left[\begin{array}{ll}
1 | 2
3 | 4
\end{array}\right]}{ }
\end{array}
\]
In this case $a=1, b=2, c=3, d=4$
Example
If $\left[\begin{array}{cc}2 | 3 1 | x\end{array}\right]=\left[\begin{array}{cc}y | 3 1 | 4\end{array}\right]$, find the
value of $x$ and the value of $y$ solution
Check the position of $x$ in the first matrix and its corresponding pesitum in the second matrix.
$x=4, y=2$
Try
If $\left[\begin{array}{ccc}6 | -3 | 1 0 | m | n 4 | -1 | -2\end{array}\right]=\left[\begin{array}{ccc}6 | -3 | p 2 | -8 | 7 4 | -1 | -2\end{array}\right]$
Find $m, n, p$ and $q$.
Example 2
Some Matrices need to be operated first unitch the left side and the right side have one matrix each.
Find $x$ if $\left[\begin{array}{l}x 2\end{array}\right]+\left[\begin{array}{l}3 4\end{array}\right]=\left[\begin{array}{l}5 6\end{array}\right]$
\[
\left[\begin{array}{l}
x
2
\end{array}\right]+\left[\begin{array}{l}
3
4
\end{array}\right]=\left[\begin{array}{l}
5
6
\end{array}\right]
\]
\[
\begin{array}{l}
{\left[\begin{array}{c}
x+3
6
\end{array}\right]=\left[\begin{array}{l}
5
6
\end{array}\right]}
\therefore x+3=5
x=5-3
\text { 2) If } x=2
{\left[\begin{array}{cc}
1 | -3
2 | -4
\end{array}\right]-\left[\begin{array}{cc}
e | 0
5 | -10
\end{array}\right]=\left[\begin{array}{cc}
-1 | -3
-3 | 2 f
\end{array}\right]}
\end{array}
\]
Find the value of $e$ and the value of $f$ (3)
Solution:
The left hand side should remoun with a single matrix.
\[
\begin{array}{l}
{\left[\begin{array}{cc}
1-e | -3+0
2-5 | -4-(-10)
\end{array}\right]=\left[\begin{array}{cc}
-1 | -3
-3 | 2 f
\end{array}\right]}
{\left[\begin{array}{cc}
1-e | -3
-3 | 6
\end{array}\right]=\left[\begin{array}{cc}
-1 | -3
-3 | 2 f
\end{array}\right]}
\end{array}
\]
Now equate the arresponding values
\[
\begin{array}{ll}
1-e=-1 | 6=2 f
-e=-i-1 | \frac{e}{2}=\frac{1 f}{2}
-e=-2 | f=3
\frac{-e}{-1}=\frac{-2}{-1} | f=3
e=2 |
\therefore e=2, f=3 | \end{array}
\]
Actwity 2.
Find the value of $x$ and $y$ "
\[
\text { 1) }\left[\begin{array}{cc}
-1 | -1
0 | 6
\end{array}\right]-\left[\begin{array}{cc}
x | 8
-2 | 4 …