Practice Midterm 1

# Practice Midterm 1 - Math 225 Spring 2008 G Rosen Practice...

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Math 225 Spring 2008 G. Rosen Practice Problems for First Midterm 1. Consider the linear system given by 2345 3664 5 xxxx ++= 12345 37 858 9 xxxxx +−+= 12 345 3 9 12 9 6 15 xx x +− + = a. Write the system in the form Ax = b for some matrix A and some vector b . b. What is the augmented matrix A # for this system. c. Put this system in Row Echelon Form. d. What is the rank( A ) and what is the rank( A # ). e. How many solutions does the system have. f. Identify any free and bounded variables. g. What is the corresponding homogeneous system. h. If the system does have solutions write the general solution in the form of the general solution to the homogeneous system plus a particular solution to the non-homogeneous system and identify each part. 2. Given the matrix A and vector b 2 35 1 25 1 A −− ⎡⎤ ⎢⎥ =− ⎣⎦ 7 5 2 b = a. Find an LU decomposition for A b. Compute det( A ) by cofactor expansion, using the definition of determinant, and by using the LU decomposition found in part a.

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## This note was uploaded on 02/28/2008 for the course MATH 225 taught by Professor Guralnick during the Spring '07 term at USC.

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Practice Midterm 1 - Math 225 Spring 2008 G Rosen Practice...

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