Question

The following system of equations $3x-7y+5z=3;3x+y+5z=7$ and $2x+3y+5z=5$

• A. consistent with trivial solution
• B. consistent with unique non trivial solution
• C. consistent with infinite solution
• D. inconsistent with no solution

Answer 1

Answer: (A)

consistent with trivial solution

$\Delta =|3-75315235|$

applying $R_1\to R_1-R_2$

$\Delta =|0-80315235|$

Now opening along $R_1$, we get

$\Delta =8\times 5=40\ne 0$

$\Delta y=|335375255|=-20\ne 0$

So, $\Delta x\ne 0,\Delta z\ne 0$

Thus consistent and with trivial solution.