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# examples of matrices word problems

Question:Last problem of online hw... thanks A dietitian at a hospital wants a patient to have a meal that has 68 grams of protein, 71 grams of carbohydrates, and 115.5 milligrams of vitamin A. The hospital food service tells the dietitian that the dinner today is salmon steak, baked eggs, and acorn squash. Each serving of salmon steak has 20 grams of protein, 10 grams of carbohydrates, and 1 milligram of vitamin A. Each serving of baked eggs contains 15 grams of protein, 3 grams of carbohydrates, and 25 milligrams of vitamin A. Each serving of acorn squash contain 4 grams of protein, 25 grams of carbohydrates, and 32 milligrams of vitamin A. How many servings of each food should the dietitian provide for the patient?

Answers:I worked out your problem using a math program. The result is a PDF file stored here... https://docs.google.com/fileview?id=0B93wLOqLZwn_ZTU2NzMyOTgtZTIzYS00NGVmLWI1MWMtY2Q2M2YyZDUzZTAx&hl=en&authkey=CKj4mpYD Hope this helps

Question:1) a theater group is to put on four performances of its latest production. each tick for a friday or saturday evening show iwll cost $10. each ticket for a saturday or sunday matinee will coast$7. write a 3x2 matrix to organize this information. 2) quadrilateral WXYZ with vertices W(-4,2), X(-1,4), Y(6,-1) and Z(-2,-3) is translated so that W' is at (5,-2). find the coordinates of X', Y', and Z'.

Question:Ugh I've hated matrices even in algebra lol. 1. Okay, first Im just really confused on how to multiply matrices. Like how do I multiply a 2x3 by a 3x2. I know how to multiply matrices when both are 2x2, but what about when one is 2x3 and the 2nd is 3x2? Or any other types? Like do you use the same steps? 2. In the book, it says "The matrices are both 2x2, so their product is defined. Use the following steps to find the elements of the product matrix." So what does it mean that it's defined? And relating to question 1, do I use these steps for solving ALL matrices multiplication problems? 3. Lastly, I was having trouble setting this problem up. "Two art classes are buying supplies. A brush is $4 and paints are$10. Each class can only spend \$225. Use matrix multiplication to find the max # of brushes class A can buy and max # paints class B can buy." I've tried several times, but it always comes out wrong.... I'm not asking for the answer, but how to set it up Thanks for any help!:)

Answers:1 and 2) It's kind of hard to explain by typing. Your first and second questions kind of go along with each other, so I'll answer them together. The product of 2 matrices is only defined if the first one is an m x k matrix and the second is a k x n (or simply, the number of columns of the first matrix is equal to the number of rows of the second matrix). The product of an mxk and kxn matrix will be an mxn matrix. In your example, the 2x3 matrix has 2 rows and 3 columns, and the 3x2 matrix has 3 rows and 2 columns, so #columns of the first matrix = #rows of the second matrix. That means the product is defined. The product will be a 2x2 matrix. I'll write an example and explain using that. Let A = | 5 2 3 | | 4 6 5 | Let B = | 1 3 | | 9 2 | | 8 6 | Now let's find what AB is. We know that it's a 2x2 matrix. AB = | __ __ | | __ __ | We need to find what each of the elements are. To figure out what goes in the first position, look at the column and row number. It's in row 1 and column 1. We want to take row 1 of A, and take the dot product of row 2 of B. I hope you know how to find the dot product. If not, I'll show you here. First, write out the things you're multiplying as vectors. Row 1 of A = <5, 2, 3> Column 1 of B = <1, 9, 8> To find the dot product, you just have to multiply the first elements in each vector and add that to the product of the second elements of each vector, and add that to the product of the third elements of each vector. In other words, do this... <5, 2, 3><1, 9, 8> = 5*1 + 2*9 + 3*8 = 5 + 18 + 24 = 47 This is the first element in the new matrix. AB = | 47 __ | | __ __ | You'll do the same thing to find the other elements. The second element is in the first row and second column, so you need the dot product of the first row of A and the second column of B (it's always row of first matrix and column of second matrix, make sense?). I'll finish working this one out, and sorry the explanation is so long. AB = | 5*1+2*9+3*8 5*3+2*2+3*6 | | 4*1+6*9+5*8 4*3+6*2+5*6 | = | 47 37 | | 98 54 | I hope that helps. Try to follow the steps. 3) I have no idea how to do this. I'm sure it's simple, but I've never done a problem like that before. I'm in linear algebra =P

Question:and used to solve problems in real life, someone said for example that polynomials cannot be used for problem solving . Is this true or not ?

Answers:Whoever told you that is misinformed. I am a physics major and it is amazing how often basic algebra can lead to major errors in calculations. Polynomials come into play often as well, where you have several different types. About every day I hear or have to use a Taylor polynomial to assist in solving a problem. Polynomials come into effect especially when dealing with wave functions such as in quantum mechanics. Matrices are especially important to physics because they are essentially vectors, and systems of equations are important because they can be graphed. The basics of graphs start in algebra, and I personally wished I would had put more emphasis on learning to graph things better, because graphs play a major effect in all the sciences. A complex real world problem may not be solved strictly using algebra, but whatever other math techniques are used, are dependent on algebra. So take it serious, it will really help make life a lot easier when you really learn the foundations.