1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider the system of equations a1 x+b1 y+c1 z=d1 a2 x+b2 y+c2 z=d2 a3 x+b3 y+c3 z=d3 This system of equations can be written as A X=B, where A=[a1 b1 c1 a2 b2 c2 a3 b3 c3] . X=[x y z] and B=[d1 d2 d3]. If A is singular and ( operatornameadj A) B=0, then the system A X=B has

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Q. Consider the system of equations
$a_1 x+b_1 y+c_1 z=d_1 $
$a_2 x+b_2 y+c_2 z=d_2 $
$a_3 x+b_3 y+c_3 z=d_3$
This system of equations can be written as $A X=B$, where $A=\begin{bmatrix}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{bmatrix} . X=\begin{bmatrix}x \\ y \\ z\end{bmatrix}$ and $B=\begin{bmatrix}d_1 \\ d_2 \\ d_3\end{bmatrix}$.
If $A$ is singular and $(\operatorname{adj} A) B=0$, then the system $A X=B$ has

Determinants

Solution:

If $A$ is a singular matrix, then $|A|=0$ and if $(\text{adj} A) B=O$, then the system may be either consistent or inconsistent according as the system have either infinitely many solutions or no solution.