The correct answer is FALSE.
A multivariate Gaussian is a probability distribution that describes the joint distribution of a set of random variables. The univariate Gaussian is a probability distribution that describes the distribution of a single random variable.
A linear combination of the components of a multivariate Gaussian is a linear combination of the random variables that make up the multivariate Gaussian. This means that the linear combination is a new random variable that is a linear combination of the original random variables.
The distribution of a linear combination of random variables is not necessarily the same as the distribution of any of the original random variables. In particular, the distribution of a linear combination of the components of a multivariate Gaussian is not necessarily a univariate Gaussian.
For example, consider a multivariate Gaussian with two components, $X$ and $Y$. The distribution of $X$ is a univariate Gaussian, and the distribution of $Y$ is a univariate Gaussian. However, the distribution of $X+Y$ is not a univariate Gaussian. The distribution of $X+Y$ is a bivariate Gaussian.
In general, the distribution of a linear combination of the components of a multivariate Gaussian is a multivariate Gaussian. However, the distribution of a linear combination of the components of a multivariate Gaussian is not necessarily a univariate Gaussian.