Suppose we have $p$ random variates :- $X_1, \cdots , X_p$. $n$ observations involving each random variable are made . Thus, the $jth $ trial or $jth$ observation is a vector of the form : $[x_{j1},x_{j2},\cdots, x_{jp}]^T$
where $x_{ji}$ means the value in the $jth$ trial for the $ith $ random variable.
Let matrix $X = [X_{.,1} ~~ X_{.,2} ~~ \cdots X_{.,p}]_{n \times p}$
Now, if we wish to investigate the linear combination of the $p$ variates, I believe the expression should be
$$c^T_{1 \times p} ~X^T_{p \times n} = c_1 X_1 + \cdots c_pX_p~~ $$
where $X_i$ is the $ith$ row of $X$ and represents the $ith$ trial.
But, my textbook multivariate statistical analysis by Richard Johnson seems to have a typo here in the image attached below. Could Someone please confirm the same? 