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assig4_2011

# assig4_2011 - n orthogonal to a b and c 4 A factory...

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Math 152, Spring 2011 Assignment #4 Notes: Each question is worth 5 marks. Due in class: Monday, January 31 for MWF sections; Tuesday, Febru- ary 1 for TTh sections. Solutions will be posted Tuesday, February 1 in the afternoon. No late assignments will be accepted. 1. Let a = ± 1 2 3 4 ² , b = ± - 1 2 - 3 - 4 ² , c = ± 2 4 6 10 ² , v = ± 1 0 1 0 ² . Consider the problem of determining if v can be ex- pressed as a linear combination of a , b and c : v = s a + t b + u c . (a) Find a system of linear equations describing this problem. (Do not solve it.) (b) Find the augmented matrix of this system. (c) Write down a MATLAB command that assigns this augmented matrix to the variable A . 2. The augmented matrix 1 4 2 7 2 | - 6 0 0 2 - 5 - 1 | 3 0 0 0 0 1 | 7 is in echelon form, but not in reduced echelon form. (a) Bring the matrix to the reduced row echelon form. (b) Find the general solution to the corresponding system of linear equations in the parametric form. 3. Let a , b and c be as in Problem 1. Find all vectors

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Unformatted text preview: n orthogonal to a , b and c . 4. A factory produces four types of cookies: A, B, C, and D. Ingredients needed to make one box of cookies of each type are given in the table: A B C D ﬂour (cups) 3 6 3 6 butter (lb.) 1 2 1 3 sugar (cups) 2 5 3 2 eggs 1 3 2 4 chocolate (lb.) 2 3 2 1 During one hour of operation, the following amounts of ingredients were used: 21 cups of ﬂour, 9 lb. of butter, 11 cups of sugar, 12 eggs, 8 lb. of chocolate. Find how many boxes of each type were produced during that hour. 5. A system of linear equations has the following augmented matrix: 1 4-2 | 1-1 1-7 7 | 2 2 3-1 c | 11 , where c is some constant. (a) For which c does the system have at least one solution? (b) Express the general solution of the system in parametric form. There should be diﬀerent cases depending on the value of c ....
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assig4_2011 - n orthogonal to a b and c 4 A factory...

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