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In this paper we discuss the issue of linear algebra on the investment portfolio optimization models. It was assumed that stock returns are analyzed have a certain distribution, so that the mean and variance and covariance between the separation can be determined. Return of some stock used to form a vector averaging, and the number of shares used as the basis to form a unit vector. While the variance of each stock as well as the covariance between stocks, is used to form a covariance matrix. The investment portfolio was formed consisting of several stocks, in order to maximize the expected return and minimize risk. The portfolio optimization was performed using linear algebra approach. The result is a formula used to determine the optimum composition of the portfolio weights. The resulting formula is very useful for the analysis of the investment portfolio optimization.