Question

The system $x + y - 4z = 2$, $3x + y + 5z = 7$, $2x + 3y + z = 5$ has

• A. infinite number of solutions
• B. unique solution
• C. trivial solution
• D. no solution

Hint:

If determinant of coefficient matrix is non-zero, system has unique solution.

Answer 1

The Correct Option is B

Step 1: Write in matrix form $AX = B$. Compute determinant: $\begin{vmatrix} 1 & 1 & -4 \\ 3 & 1 & 5 \\ 2 & 3 & 1 \end{vmatrix} = 1(1-15) - 1(3-10) -4(9-2) = -14 - (-7) -4(7) = -14+7-28 = -35 \neq 0$.}
Step 2: Non-zero determinant means unique solution.}