Consider the following system of linear equations
\[\left[ {\begin{array}{*{20}{c}}
2&1&{ - 4} \\
4&3&{ - 12} \\
1&2&{ - 8}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{\text{x}} \\
{\text{y}} \\
{\text{z}}
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
\alpha \\
5 \\
7
\end{array}} \right]\]
Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of \[\alpha \], does this system of equations have infinitely many solutions?
A. 0
B. 1
C. 2
D. infinitely many
Answer: Option B
This Question Belongs to Engineering Maths >> Linear Algebra
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