How Should I Approach Solving This Linear Algebra Matrix Problem?

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The discussion centers on solving a linear algebra matrix problem presented via an image link. The user has constructed a matrix from given data and is unsure how to proceed. They mention the possibility of row reduction but express confusion about determining the types of solutions, such as single, infinite, or no solutions. The consensus suggests performing row reduction to identify values of lambda that lead to no solutions. This approach will clarify the conditions under which the matrix has different types of solutions.
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i got this question:

http://img525.imageshack.us/my.php?image=29469701vt4.gif

in the link i showed that i tried to build a matrices from the given data

what should i do with this matrix?

i can do row reduction
but then i have single solution,infinite number of solutions ,no solutions

what should i do in order to solve this question??
 
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Do a row reduction and see for which values of lambda there is no solution.
 

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