Q155
Consider the following system of linear equations \[ [ array*20c 2&1& - 4 \\ 4&3& - 12 \\ 1&2& - 8 array ] [ array*20c x \\ y \\ z array ] = [ array*20c \\ 5 \\ 7 array ]\] Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of \[ \], does this system of equations have infinitely many solutions?
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 , does this system of equations have infinitely many solutions?
\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 , does this system of equations have infinitely many solutions?
A.
0
B.
1
AnswerC.
2
D.
infinitely many
Answer: Option B
Solution
Answer: Option B
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