gibson:teaching:fall-2014:math445:hw3solns

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+ | ====== Math 445 HW3 solutions ====== | ||

+ | <code> | ||

+ | John Gibson | ||

+ | Math 445 | ||

+ | HW3 solutions | ||

+ | Oct 7, 2014 | ||

+ | |||

+ | |||

+ | Problem 1: Given the vectors x=[3 7 2 9 0] and y=[7 10 2 8 13], what | ||

+ | would be the Matlab output for the following expressions? Think | ||

+ | through what the answer should be, write it down, and then try it out | ||

+ | in Matlab. If you got anything wrong, figure out what your mistake was | ||

+ | and why Matlab gave the answer it did. | ||

+ | |||

+ | (a) x > y | ||

+ | [0 0 0 1 0] | ||

+ | |||

+ | (b) y < x | ||

+ | [0 0 0 1 0] | ||

+ | |||

+ | (c) x == y | ||

+ | [0 0 1 0 0] | ||

+ | |||

+ | (d) x <= y | ||

+ | [1 1 1 0 1] | ||

+ | |||

+ | (e) y >= x | ||

+ | [1 1 1 0 1] | ||

+ | |||

+ | (f) x & y | ||

+ | [1 1 1 1 0] | ||

+ | |||

+ | (g) x & (~y) | ||

+ | [0 0 0 0 0] | ||

+ | |||

+ | (h) (~x) & (y) | ||

+ | [0 0 0 0 1] | ||

+ | |||

+ | (i) x | y | ||

+ | [1 1 1 1 1] | ||

+ | |||

+ | (j) xor(x,y) | ||

+ | [0 0 0 0 1] | ||

+ | |||

+ | (k) (x > y) & (y < x) | ||

+ | [0 0 0 1 0] | ||

+ | |||

+ | Problem 2: Write down Matlab expressions for the following. You can | ||

+ | assume that a,b,c are logical variables, x,y,z are double-precision | ||

+ | numbers, u,v,w are vectors of the same dimension, and A,B,C are | ||

+ | matrices of compatible sizes. | ||

+ | |||

+ | (a) Both a and b are true. | ||

+ | a && b | ||

+ | |||

+ | (b) Neither a nor b is true. | ||

+ | ~a && ~b | ||

+ | |||

+ | (c) Either a and b are both true, or b and c are both false. | ||

+ | (a && b) || (~b && ~c) | ||

+ | |||

+ | (d) Either x equals y, or x is not equal to z. | ||

+ | (x == y) || (x ~= z) | ||

+ | |||

+ | (e) x, y, and z are all equal. | ||

+ | (x == y) && (x == z) && (y == z) | ||

+ | |||

+ | (f) None of the components of u equal the corresponding components of v. | ||

+ | ~any(u == v) | ||

+ | |||

+ | (g) Each component of u is the same as either the same component of v or w. | ||

+ | all(u == v) | ||

+ | |||

+ | (h) The vector whose components are the polynomial 3u^2 - 5u + 6 evaluated | ||

+ | at each of the components of u. | ||

+ | 3*u.^2 - 5*u + 6 | ||

+ | |||

+ | (i) The matrix product AB. | ||

+ | A*B | ||

+ | |||

+ | (j) The matrix whose elements are the product of the elements of A and B. | ||

+ | A.*B | ||

+ | |||

+ | Problem 3: A theater has a seating capacity of 900 and charges $2.50 | ||

+ | for children, $4 for students, and $5.50 for adults. At a certain | ||

+ | screening with full attendance, there were half as many adults as | ||

+ | children and students combined. The total money brought in was | ||

+ | $3825. How many children, students, and adults attended the show? | ||

+ | show? | ||

+ | |||

+ | The equations are | ||

+ | |||

+ | c + s + a = 900 | ||

+ | 2.5c + 4s + 5.5a = 3825 | ||

+ | 0.5(c + s) = a | ||

+ | |||

+ | or | ||

+ | |||

+ | c + s + a = 900 | ||

+ | 2.5c + 4s + 5.5a = 3825 | ||

+ | 0.5c + 0.5s - a = 0 | ||

+ | |||

+ | To put this in matrix-vector notation, let the column vector x | ||

+ | have components [c s a]'. Then | ||

+ | |||

+ | A = [1 1 1; 2.5 4 5.5; 0.5 0.5 -1]; | ||

+ | b = [900 3825 0]'; | ||

+ | |||

+ | x = A\b | ||

+ | |||

+ | x = | ||

+ | 150 | ||

+ | 450 | ||

+ | 300 | ||

+ | |||

+ | So 150 children, 450 students, and 300 adults attended the show. | ||

+ | </code> |

gibson/teaching/fall-2014/math445/hw3solns.txt ยท Last modified: 2014/10/07 10:43 by gibson