math111hw1 - 1 2 2 2 3 Ch1.2 # 4 Row reduce the following...

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MATH111 HW 1 Due Date: 17th, Sept, 2007 (Mon) Please hand in your HW to me in my tutorial session or Put it in the collection box outside MATH dept (Rm 3461, Lift 25-26) Ch1.1 # 2 Solve the following system by using elementary row operations on the equations or on the augmented matrix. Follow the systematic elimiation procedure described in the textbook. ± 2 x 1 + 4 x 2 = - 4 5 x 1 + 7 x 2 = 11 Ch1.1 # 11 Solve the following system. x 2 + 4 x 3 = - 5 x 1 + 3 x 2 + 5 x 3 = - 2 3 x 1 + 7 x 2 + 7 x 3 = 6 Ch1.1 # 12 Solve the following system. x 1 - 3 x 2 + 4 x 3 = - 4 3 x 1 - 7 x 2 + 7 x 3 = - 8 - 4 x 1 + 6 x 2 - x 3 = 7 Ch1.1 # 16 Determine if the following system is consistent. Do not completely solve the system. x 1 - 2 x 4 = - 3 2 x 2 + 2 x 3 = 0 x 3 + 3 x 4 = 1 - 2 x 1 + 3 x 2 + 2 x 3 + x 4 = 5 Ch1.1 # 22 Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. ² 2 - 3 h - 6 9 5 ³ Ch1.2 # 2 Determine which of the following matrices are in reduced echelon form and which others are only in echelon form. a. 1 1 0 1 0 0 1 1 0 0 0 0 b. 1 1 0 0 0 1 1 0 0 0 1 1 1
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c. 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 d. 0 1 1 1
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Unformatted text preview: 1 2 2 2 3 Ch1.2 # 4 Row reduce the following matrix to reduced echelon form. Circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns. 1 3 5 7 3 5 7 9 5 7 9 1 Ch1.2 # 10 Find the general solutions of the systems whose augmented matrix is given below: ± 1-2-1 3 3-6-2 2 ² Ch1.2 # 12 Find the general solutions of the systems whose augmented matrix is given below: 1-7 6 5 1-2-3-1 7-4 2 7 Ch1.2 # 33 Find the interpolating polynomial p ( t ) = a + a 1 t + a 2 t 2 for the data (1,12), (2,15), (3,16). That is, find a , a 1 , and a 2 such that a + a 1 (1) + a 2 (1) 2 = 12 a + a 1 (2) + a 2 (2) 2 = 15 a + a 1 (3) + a 2 (3) 2 = 16 2...
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This note was uploaded on 04/03/2010 for the course MATH math111 taught by Professor Cheng during the Spring '07 term at HKUST.

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math111hw1 - 1 2 2 2 3 Ch1.2 # 4 Row reduce the following...

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