Teacher/User Name: DEMO Name:__________________________
Practice Problems
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Period: ________ Date: ____________

 
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Solve:

1) Do the three lines have a common point of intersection? Why or why not?
-5x1+ 7x2 = -10
   2x2+ 7x3 = -9
-5x1- 28x3 = 23

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2) Do the three planes have at least one common point of intersection? Why or why not?
6x1- 9x2- 8x3 = -9
- x1- 9x2- 4x3 = 2
7x1- 4x3 = -11
3) Determine all values of b1 and b2 that will make the following augmented matrix consistent:





-9 b1 




-16 18 b2 

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4) Do these equations have at least one solution? Why or why not?
-10x1+ 9x2+ 2x3 = -1
-9x1- 6x2-  x3 = 9
-7x1- 36x2- 7x3 = 26

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