Consider the system of linear equations; x1 + 2x2 + x3 = 3 2x1 + 3x2 + x3 = 3 3x1 + 5x2 + 2x3 = 1 The system has

Question

Consider the system of linear equations; x1 + 2x2 + x3 = 3 2x1 + 3x2 + x3 = 3 3x1 + 5x2 + 2x3 = 1 The system has (A) exactly 3 solutions (B) a unique solution (C) no solution (D) infinite number of solutions

Tardigrade Admin · Accepted Answer

D = |1&2&1 2&3&1 3&5&2| = 0 D1 = |3&2&1 3&3&1 1&5&2|≠0 ⇒ Given system, does not have any solution. ⇒ No solution

Q. Consider the system of linear equations;
$x_{1} + 2 x_{2} + x_{3} = 3$
$2 x_{1} + 3 x_{2} + x_{3} = 3$
$3 x_{1} + 5 x_{2} + 2 x_{3} = 1$
The system has

exactly 3 solutions

a unique solution

no solution

infinite number of solutions

$D = ∣ ∣ 123235112 ∣ ∣ = 0$
$D_{1} = ∣ ∣ 331235112 ∣ ∣ \neq = 0$
$\Rightarrow$ Given system, does not have any solution.
$\Rightarrow$ No solution

Q. Consider the system of linear equations; x1​+2x2​+x3​=3 2x1​+3x2​+x3​=3 3x1​+5x2​+2x3​=1 The system has