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 Math 166  Top In Contemp Math Ii
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Page 1 WIR Math 166 copyright Joe Kahlig 09C Week in Review Additional Chapter 5 Material Section 5 2 Matrix Multiplication if A is a mxn matrix and B is a nxp matrix then the matrix AB has a size of mxp note the number of columns of A equals the number of rows of B identity matrix In size nxn all zeros except for a1 1 a2 2 a3 3 1 A 7 2 4 6 5 0 B 9 1 3 0 2 8 1 C 2 2 3 5 0 D x 1 2 5 1 Use the above matrices to compute the following a AC b BD c DB d D 2 1 0 e 2 0 1 0 0 1 4 8 0 0 2 3 0 0 1 5 1 1 1 0 0 2 f 0 1 0 0 0 0 1 8 4 3 1 2 8 0 5 5 2 A dietitian plans a meal around two foods The number of units of vitamin A and vitamin C in each ounce of these foods is represented by the matrix M Food I Vitamin A 30 M Vitamin C 7 Food II 90 45 Food I B h 5 Food II 2 Food I i L h 9 Food II 4 i The matrices B and L represent the amount of each food in ounces consumed by the girl at breakfast and lunch respectively Explain the meaning of the entries in these computations a LM h 298 990 i b MB T 330 125 WIR Math 166 copyright Joe Kahlig 09C Page 2 Section 5 3 The inverse of a Matrix the matrix must be square NOT all square matrices have an inverse the inverse of A is denoted A 1 AA 1 A 1 A I A system of equations may be written as a matrix equation AX B A is the coefficient matrix X is the variable matrix If A has an inverse then the solution is X A 1 B Matrix A not having an inverse does not imply that the system of equations has no solution It means that you need to try another method to solve the problem 3 If A 5 1 5 2 find A 1 1 1 find A 1 2 2 1 5 If A 4 2 2 1 1 3 find A 1 2 6 Determin 1 A 0 0 matrices A and B are inverses of each other 1 2x 2 4 5x 1 2 B 0 0 2 5 2 1 4 If A 3 2 2 1 if the 2 x 5 2 2 1 2x z 2 7 Answer the following using this system of equations 2x y z 1 3x y z 4 a Write down the coefficient matrix b Write the system of equations as a matrix equation c Solve the system of equations using matrices 8 True or False A system of equations is represented by the matrix equation AX B If the coefficient matrix A does not have an inverse then the system of equations does not have a solution 9 Solve for the matrix X Assume that all matrices are square and all needed inverses are possible a BX E CX b XJ XA K
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