Expectation and Variance of linear transformation of multivariate random variable

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Calculation of expectation and variance

I've been reading "Mathematics for Machine Learning: https://mml-book.com." In the book, I couldn't see the deviation of multivariate expectation (6.50) and variance (6.51). They seem to be calculated based on the definition of the mean and covariance.

I would like to appreciate if anybody helps me understand this.