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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
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
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.