Find the value of
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Step-by-step explanation:
rs
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Matrices
Use $$\begin{matrix}…\end{matrix}$$ In between the \begin and \end, put the matrix elements. End each matrix row with \\, and separate matrix elements with &. For example,
$$
\begin{matrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2 \\
\end{matrix}
$$
produces:
1 x x2 1 y y2 1 z z2
MathJax will adjust the sizes of the rows and columns so that everything fits.
To add brackets, either use \left…\right as in section 6 of the tutorial, or replace matrix with pmatrix ( 1 2 3 4 ), bmatrix [ 1 2 3 4 ], Bmatrix { 1 2 3 4 }, vmatrix | 1 2 3 4 |, Vmatrix ‖ 1 2 3 4 ‖.
Use \cdots ⋯ \ddots ⋱ vdots ⋮ when you want to omit some of the entries:
( 1 a1 a
2
1
⋯ a
n
1
1 a2 a
2
2
⋯ a
n
2
⋮ ⋮ ⋮ ⋱ ⋮ 1 am a
2
m
⋯ a
n
m
)
For horizontally "augmented" matrices, put parentheses or brackets around a suitably-formatted table; see arrays below for details. Here is an example:
[ 1 2 3 4 5 6 ]
is produced by:
$$ \left[
\begin{array}{cc|c}
1&2&3\\
4&5&6
\end{array}
\right] $$
The cc|c is the crucial part here; it says that there are three centered columns with a vertical bar between the second and third.
For vertically "augmented" matrices, use \hline. For example
( a b c d 1 0 0 1 )
is produced by
$$
\begin{pmatrix}
a & b\\
c & d\\
\hline
1 & 0\\
0 & 1
\end{pmatrix}
$$
For small inline matrices use \bigl(\begin{smallmatrix} ... \end{smallmatrix}\bigr), e.g. ( a b c d ) is produced by:
$\bigl( \begin{smallmatrix} a