Zakrajšek was born in Ljubljana, Yugoslavia (today Slovenia). He became an orphan even before he started to attend school. He went to elementary school and gymnasium in Jesenice. He was a good schoolboy and he showed his talent and abilities very early. He graduated from technical mathematics at the Department of mathematics and physics of then Faculty for natural sciences and technology (FNT) of the University of Ljubljana. He received his Master's degree at the University of Zagreb with a work Numerična realizacija Ritzovega procesa (Numerical realization of the Ritz process) and his doctorate in 1978 in Ljubljana with a dissertation O invariantni vložitvi pri reševanju diferencialnih enačb (About the invariable embeding in solving of differential equations).
Professor Zakrajšek was one of the pioneers of computer science in Slovenia. He became an expert about the first computers of the University of Ljubljana, the Zuse Z-23 and its successor the IBM 1130. Later on he participated in the development of programming languages, tools and operating systems. He wrote textbooks and manuals for them simultaneously: for Z-23 assembler, Algol, Fortran, Algol 68, Pascal, for domestic structran. In 1982 he set off for United States and he became the manager of the programming equipment at the firm Cromemco. In 1994 he returned to homeland, where he occupied professorship again. With his advocacies about the C and open operating systems, that is unix and linux, he helped to modernize the lessons of computer science. He became an expert again for TeX, LaTeX and Matlab.
Beside his computer scientifical skills he was also an excellent mathematician with a broad profile. He taught and solved problems from many fields: the usage of mathematics in natural and social sciences, statistics, mechanics, classical applied mathematics, discrete mathematics, graph and network theory, linear programming, operational researches, numerical analysis.