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Determine the values of $\lambda $ so that the equations $x+y+z=1 \; ; \; x+2y+4z=\lambda \; ; \; x+4y+10z=\lambda^2$ have solution and solve them completely in each case.
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written 7.9 years ago by
teamques10
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Writing given equations in matrix form AX=B
$ \therefore \left[ \begin{array}{ccc} 1& 1& 1\\ 1& 2& 4\\ 1& 4& 10 \end{array}\right] \left[ \begin{array}{c} x\\ y\\ z \end{array}\right] \;=\; \left[ \begin{array}{c} 1\\ \lambda\\ \lambda^2 \end{array}\right] \\ \; \\ \; \\ \; \\ R_2 \rightarrow R_2 - R_1 , R_3 \rightarrow R_3-R_2 …
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