Explain why it is important to be able to perform matrix operations by hand when a calculator can do them for you.

Answer:

It is important to be able to perform matrix operations by hand because calculators may not always be available, such as on certain tests or if the calculator dies. Finding an inverse or doing other operations by hand also helps you understand the process instead of just getting an answer. Calculators may show decimal approximations rather than exact fractions. For small or simple matrices, working by hand can sometimes be faster. Finally, a matrix could contain a variable, which many calculators cannot handle easily.