For the system of linear equations:

x – 2y = 1, x – y + kz = -2, ky + 4z = 6, k $\in R,$  

Consider the following statements:

(A) The system has unique solution if $k\ne 2,k\ne -2.$  

(B) The system has unique solution if k = -2.

(C) The system has unique solution if k = 2.

(D) The system has no solution if k = 2.

(E) The system has infinite number of solutions if $k\ne -2.$  

Which of the following statements are correct?

<p>x – 2y = 1, x – y + kz = -2, ky + 4z = 6</p><p>x – 2y + 0. z – 1 = 0</p><p>x – y + kz + 2 = 0</p><p>0x + ky + 4z – 6 = 0</p><p>0x + ky + 4z – 6 = 0</p><p><span contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>Δ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mtable> <mtr columnalign="center"> <mtd columnalign="center"> <mn>1</mn> </mtd> <mtd columnalign="center"> <mo>−</mo> <mn>2</mn> </mtd> <mtd columnalign="center"> <mn>0</mn> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <mo>−</mo> <mn>2</mn> </mtd> <mtd columnalign="center"> <mo>−</mo> <mn>1</mn> </mtd> <mtd columnalign="center"> <mi>k</mi> </mtd> </mtr> <mtr columnalign="center"> <mtd columnalign="center"> <mn>6</mn> </mtd> <mtd columnalign="center"> <mi>k</mi> </mtd> <mtd columnalign="center"> <mn>4</mn> </mtd> </mtr> </mtable> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mo>−</mo> <mrow> <mo> (</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo> (</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p><p>For no solution</p><p><span contenteditable="false"> <math> <mrow> <mi>Δ</mi> <mo>=</mo> <mn>0</mn> <mo>, </mo> <msub> <mrow> <mi>Δ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>≠</mo> <mn>0</mn> </mrow> </math> </span></p><p>k = 2</p>

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