2004Spring20MidtermI-sol

2004Spring20MidtermI-sol - Midterm Problems Problem 1 Let...

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Unformatted text preview: Midterm Problems Problem 1 Let In[1]:= A = J 1 2- 1- 1 N B = J 3 2 1 N Out[1]= 88 1, 2 < , 8- 1,- 1 << Out[2]= 88 3, 0 < , 8 2, 1 << Find In[6]:= 3 A + 2 B MatrixForm A .B MatrixForm A. A. Transpose @ B D MatrixForm Out[6]//MatrixForm= J 9 6 1- 1 N Out[7]//MatrixForm= J 7 2- 5- 1 N Out[8]//MatrixForm= J- 3- 2- 1 N Problem 2 Find the parametric form to the general solution to the system of linear equations 2 x 1 + 4 x 2 + x 4 = 2; x 1 + 2 x 2 + x 3 + 2 x 4 = 4; 3 x 1 + 6 x 2 + 2 x 3 + x 4 = 4; Solution. The augmented matrix of this system of linear equations is In[11]:= M2 = i k j j j j j j j 2 4 1 2 1 2 3 2 4 3 6 2 1 2 y { z z z z z z z Out[11]= 88 2, 4, 0, 1, 2 < , 8 1, 2, 3, 2, 4 < , 8 3, 6, 2, 1, 2 << mt1.nb 1 which has reduced row echelon form In[12]:= RowReduce @ M2 D MatrixForm Out[12]//MatrixForm= i k j j j j j j j 1 2 1 1 2 y { z z z z z z z This means the general solution takes the form x 4 = 2; x 3 = x 2 is free x 1 = - 2 x 2 Another way to write this is i k j j j j j j j j j j j j z 1 z 2 z 3 x 4 y { z z z z z z z z z z z z = i k j j j j j j j j j...
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This note was uploaded on 11/10/2009 for the course MATH 1850 taught by Professor Mihaibeligan during the Spring '09 term at UOIT.

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2004Spring20MidtermI-sol - Midterm Problems Problem 1 Let...

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