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PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH UNIVERSITI SAINS MALAYSIA ACADEMIC SESSION 2018/2019 JIM 201 – LINEAR ALGEBRA Assignment 1 : 10 % Course Manager: Assoc. Prof. Mohd. Nain Hj. Awang ANSWER ALL QUESTIONS. Due date: 30th December 2018 1. 4 − 2 5 Given that matrix A = 4 5 − 2 such that A2 + A + I = O −2 − 2 2 where I is an identity matrix 3 3 and O is a zero matrix 3 3. Determine the values of and . 2 −1 2 2. Given that matrix B = 3 −1 0 k 4 k + 2 and B = 27 . Find the value of (b) BT B 2 (a) k , where k is an integer (c ) B T B 3 B T 3 Using only elementary row operations and theorems, show that 1 a 1 b 1 c bc ca = ( a − b )( b − c )( c − a ) ab 3 −1 1 −1 3 1 0 2 4. Find −2 − 2 −4 − 5 2 2 3 1 − 1 . Hence, solve the system 0 3x + 3 y − z = 2 − 2 x − 2 y + z = −1 − 4x − 5 y + 2z = 0 5. Solve the system of equations 5 x − 3 y + 2 z = 13 − 2 x + y + 3z = −1 2x − y + 2z = 6 by using (a) the inverse method (b) the Gauss-Jordan elimination method (c) Cramer’s Rule 1 2 6. (a) Find the inverse matrix of C = 2 4 3 5 3 5 . 6 (b) The table below shows the number of boxes of milk P , Q and R which were supplied by a dairy to three houses in a village every week. House/Milk Milk P Milk Q Milk R 1st House 1 2 3 2nd House 2 4 5 3 rd House 3 5 6 The payment collected by the dairy owner from the first, second and third houses are RM130, RM 235 and RM 295 respectively. If x, y and z are the prices for each box of the milk, write a system of linear equation from the above information. Then, determine the values of x, y and z using inverse matrix. 000000000000000