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Mathematics Question on Matrices

Consider the system of linear equations x1+2x2+x3=3\[0.3em]2x1+3x2+x3=3\[0.3em]3x1+5x2+2x3=1x_1+2x_2+x_3=3\\\[0.3em] 2x_1+3x_2+x_3=3 \\\[0.3em]3x_1+5x_2+2x_3=1 The system has

A

a unique solution

B

no solution

C

infinite number of solutions

D

exactly 3 solutions.

Answer

no solution

Explanation

Solution

Adding the first two equations and subtracting the third from the sum, we get (x1+2x2+x3)+(2x1+3x2+x3)−(3x1+5x2+2x3)(x_1 + 2x_2 + x_3) + (2x_1 + 3x_2 + x_3) - (3x_1+ 5x_2 + 2x_3) = 3 + 1-1 Thus, the system of equation has no solution.