Begin Array in LaTex

Tried the equation in the image below with the following codes, but was encountering errors. Please can anybody be kind enough to help. Thanks.

\begin{array}
{p^'}_0\left( t \right) =  - \lambda {p_0}\left( t \right) + \mu {p_1}\left( t \right),\\
{p^'}_j\left( t \right) = \lambda {p_{j - 1}}\left( t \right) - \left( {\lambda  + j\mu } \right){p_j}\left( t \right) + \mu \left( {j + 1} \right){p_{j + 1}}\left( t \right)
\end{array}

-

there are several problems with the code used:

• array must be inside a math environment; this could be fixed by enclosing it in $...$

• the alignment within the array must be specified; for this, \begin{array}{l} would work.

• the primes (input as apostrophes) are defined to be superscripts, so the explicit ^ is unwanted.

• the \left ... \right for the parentheses isn't needed anywhere, since everything within them is "normal" size

• extra grouping with braces isn't needed except around the multi-element subscripts

it would be equally appropriate, and perhaps simpler, to use the align* environment from amsmath:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
p'_0 (t) &= -\lambda p_0 (t) + \mu p_1 (t),\\
p'_j (t) &=  \lambda p_{j-1} (t) - (\lambda + j\mu) p_j (t) + \mu (j+1) p_{j+1} (t)
\end{align*}
\end{document}


-

it's not really an array, so i rewrote it as a pair of aligned equations -- which is nearer to the mark (to my way of thinking).

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
p'_0( t ) &=  -\lambda {p_0}( t ) + \mu {p_1}( t ),\\
p'_j( t ) &=   \lambda {p_{j - 1}}( t ) - ( {\lambda  + j\mu } ){p_j}
( t ) + \mu ( {j + 1} ){p_{j + 1}} t )
\end{align}
\end{document}


note, i've taken off all your \left/\right things, which aren't necessary here.

-

No need for \left(...\right) for simple expressions:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{concrete}
\usepackage{amsmath}
\begin{document}

\begin{align*}
p^\prime_0(t) &=  -\lambda p_0(t) + \mu p_1(t),\\
p^\prime_j(t) &=   \lambda p_{j-1}(t) - (\lambda  + j\mu)p_j(t) + \mu (j+1)p_{j+1}(t)
\end{align*}

\end{document}


-
\begin{array}{l} % Here is the change
{p^'}_0\left( t \right) =  - \lambda {p_0}\left( t \right) + \mu {p_1}\left( t \right),\\
{p^'}_j\left( t \right) = \lambda {p_{j - 1}}\left( t \right) - \left( {\lambda  + j\mu } \right){p_j}\left( t \right) + \mu \left( {j + 1} \right){p_{j + 1}}\left( t \right)
\end{array}


l means one column with left aligned entries. BTW: \left and \right are unnecessary here.

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p^' should be p' – egreg Mar 18 '14 at 15:32