(See Solution) Use the determinant of the coefficient matrix of the following system to determine whether the system of linear equations has a unique solution.
Question: Use the determinant of the coefficient matrix of the following system to determine whether the system of linear equations has a unique solution. State clearly the theorems you are using and explain why you can use the determinant to answer the question. Show all work.
\[\begin{aligned} &x+y-z=4 \\ &2 x-y+z=6 \\ &3 x-2 y+2 z=0 \end{aligned}\]
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(Solution Library) Do the three lines 2 x_1+3 x_2=-1,6 x_1+5 x_2=0, and
![[Solution Library] Determine if b is a](/images/solutions/MC-solution-library-73675.jpg "[Solution Library] Determine if b is a linear combination of the vectors")
[Solution Library] Determine if b is a linear combination of the vectors
(See Solution) Let u=[c4 , -1 , 4] and A=[ccc2 5 -1 , 0 1 -1 , 1
![[Steps Shown] Write the following system first](/images/solutions/MC-solution-library-73677.jpg "[Steps Shown] Write the following system first as a vector equation")
[Steps Shown] Write the following system first as a vector equation
![[Solution Library] Describe the solutions of the](/images/solutions/MC-solution-library-73678.jpg "[Solution Library] Describe the solutions of the following system")
[Solution Library] Describe the solutions of the following system
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