Confusion matrix - determine the values of FP FN TP and TN
You can!

The trick is that you actually know two other critical variables: the number of positive and negative examples (P and N). You can then use them to algebraically solve for the confusion matrix:

$ recall=\frac{TP}{TP+FN}=1-\frac{FN}{P}\Rightarrow $


$ FN = P(1-recall) $


$ recall=\frac{TP}{TP+FN}\Rightarrow (recall)(TP+FN)=TP\Rightarrow TP(1-recall)=FN\Rightarrow$


$ TP=\frac{FN}{1-recall} $
or simply: $ TP=P-FN $


$ accuracy = \frac{TP+TN}{P+N}\Rightarrow (accuracy)(P+N)=TP+TN\Rightarrow $


$ TN=(accuracy)(P+N)-TP $


$ accuracy = \frac{TP+TN}{TP+TN+FP+FN}\Rightarrow (accuracy)(TP+TN+FP+FN)=TP+TN\Rightarrow $


$ FP=\frac{TP+FN}{accuracy}-TP-TN-FN $
or simply: $ FP=N-TN $