How do i interpret this correlation
No. From this correlation matrix you cannot draw the conclusion that


  as long as the student has good gpa and good gre even though his Alma Mater's prestige is low - he will get admitted in a college


The reason is that correlation is a measure of association between single pairs of variables. The conclusion you draw above - on the contrary - is based on a combination of three different variables plus the outcome variable.

If you want to get an estimation of the probability that a student will be admitted to college based on her gpa, gre and prestige the right way is to create a logistic regression model. Here's an example in R (provided that admit is a binary variable, with admit=1 indicating that the student is admitted and admit=0 that she is not admitted)

model &lt;- glm(admit ~.,family=binomial(link='logit'),data=data)


With this fitted model you can then compute the probability that a student is admitted given her particular combination of gpa, gre and prestige.