Answer: Epsom salt (magnesium sulphate) is used as a source of magnesium and if applied, is used as a side-dressing or foliar spray as needed during the growing season. Certain crops, including peppers, tomatoes and roses, sometimes benefit from the additional magnesium. Rarely is there a deficiency in soils that would require the supplementing of these nutrients and, if you're using other complete fertilizers, you're already adding magnesium and sulfur.
As you probably know, the black fabric is used to warm up the soil so that tomatoes can get a jumpstart, since they prefer a warmer soil to thrive. Did you mix the fertilizer and Epsom salts well into the soil mix before planting? Sometimes too much salt can burn sensitive plant roots and the whole plant dies. Was the soil consistently moist? Tomatoes are extremely moisture sensitive, so if the soil dried out down where the roots are, and the fabric contributed to the hot, dry soil, transplants could easily die before establishing a root system. I hope this information is helpful--if you hurry you should be able to get some more transplants into the ground! Try just one modification at a time, so you'll know what works and what doesn't! Good luck.
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