Consider the system of equations x - 2y + 3z = -1, x- 3Y - 4z = 1 and - x + Y - 2z = k

Question

For the following questions, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows' 

(a) Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I. 

(b) Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I. 

(c) Statement I is true; Statement II is false. 

(d) Statement I is false; Statement II is true.

Consider the system of equations 

x - 2y + 3z = -1,

x- 3Y - 4z = 1 

and - x + Y - 2z = k 

Statement I : the system of equations has no solution for k ≠ 3. and

Statement II : The determinant |(1, 3, -1), (-1, - 2, k), (1, 4, 1)| ≠ 0 

for k ≠ 0.  

Answer 1

The correct option (a) Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I.

Explanation:

The given system of equations can be expressed as

When k ≠ 3, the given system of equations has no solution. 

⇒ Statement I is true. Clearly, Statement II is also true as it is rearrangement of rows and columns of

Hence, option (a) is correct.