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linear algebra

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in order to grow a certain crop, it is recommended that each square foot of ground be treated with 10 units of phosphorous, 9 units of potassium, and 19 units of nitrogen, suppose that there are three brands of fertilizer on the market - say brand X, brand Y, and brand Z. One pound of brand X contains 1 unit of phosphorous, 3 units of potassium, and 4 units of nitrogen. One pound of brand Z contains only 1 unit of phosphorous and 1 unit of nitrogen.

a. Determine whether or not possible to meet exactly the recommendation by applying some combination of three brands of fertilizer. Give your reasoning.

b. if it is possible to meet the recommendation, what is the combination of the three brands that satisfies the recommendation?

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