In this paper, we study three fault tolerance techniques: data redundancy, algorithm-based fault tolerance, and pair and spare. These techniques, each individually useful, produce excitingly high levels of protection at a relatively low cost when used in combination. We first discuss the techniques separately, extending triple data redundancy to band matrix multiplication while applying algorithm-based fault tolerance to dense matrix multiplication. We then combine double data redundancy and algorithm-based fault tolerance to produce a linear array that corrects transient errors at minimal costs. Finally, we show how the above techniques can be used to implement pair and spare at half the normal cost.