6. Consider the A = LR factorization of the matrix A: A = 1 0 0 1 1 0 0 1 1 0 3 2 3 4 0 0 0 2 4 0 0 0 0 0 withou
t multiplying L and R (a) Find a basis for C(A). (b) Find a basis for R(A). (c) Find a basis for N(A). (d) Find a basis for N(AT ). (e) Write the dimension of each of these subspace.
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Answer:
First type of fruit drinks: 48 pints
Second type of fruit drinks: 32 pints
Step-by-step explanation:
Let's call A the amount of first type of fruit drinks. 55% pure fruit juice
Let's call B the amount of second type of fruit drinks. 80% pure fruit juice
The resulting mixture should have 65% pure fruit juice and 80 pints.
Then we know that the total amount of mixture will be:
Then the total amount of pure fruit juice in the mixture will be:
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:
+
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We substitute the value of A into one of the two equations and solve for B.