Question

Statement I: The system of equations 4x + 3y = 2, 8x + 6y = 5 is inconsistent.

Statement II: The system AX=B of equations is inconsistent, if |A|=0 and (adjA)B≠ 0.

• A. Both Statement I and Statement II are correct.
• B. Statement I is correct but Statement II is incorrect.
• C. Statement II is correct but Statement I is incorrect.
• D. Both Statement I and Statement II are incorrect.

Answer 1

Answer: (A)

Both Statement I and Statement II are correct.

Answer 2

Statement I:

Equations:

$$4x+3y=2, \quad 8x+6y=5.$$

Multiplying the first equation by 2 gives:

$$8x+6y=4.$$

Since $8x+6y=4 \neq 5$ from the second equation, the system is inconsistent.

Statement II:

It is known that if $|A|=0$ (i.e., $A$ is singular) then the system $AX=B$ is consistent if and only if $(\operatorname{adj}A)B=0$. Hence, if $|A|=0$ and $(\operatorname{adj}A)B \neq 0$, the system is inconsistent.

Both statements are correct.