Which one of the following statements is wrong?

If the system of equations&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced separators="|" close="}" open=""><mtable columnalign="left" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">x</mi><mo>−</mo><mi>λy</mi><mo>−</mo><mi mathvariant="normal">z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>λx</mi><mo>−</mo><mi mathvariant="normal">y</mi><mo>−</mo><mi mathvariant="normal">z</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>−</mo><mi mathvariant="normal">z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math>&nbsp;has a unique solution, then the range of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">λ</mi><mtext>&nbsp;is&nbsp;</mtext><mi mathvariant="normal">R</mi><mo>−</mo><mo>{</mo><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">b</mi><mo>}</mo></math>, &nbsp;Then the value of&nbsp; (a2 + b2) is

If the system of linear equations x+ky+3z = 0, 3x+ky-2z = 0, 2x+4y-3z = 0 has a nonzero solution (x, y, z) then&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>&nbsp;</mo><mi>z</mi></mrow><msup><mi>y</mi><mn>2</mn></msup></mfrac></math>= &nbsp;

<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">b</mi><mo>,</mo><mi mathvariant="normal">c</mi><mtext>&nbsp;are distinct real numbers, not equal to one. If&nbsp;</mtext><mi>ax</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>+</mo><mi mathvariant="normal">z</mi><mo>=</mo><mn>0</mn><mo>,</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi>by</mi><mo>+</mo><mi mathvariant="normal">z</mi><mo>=</mo><mn>0</mn><mtext>, and&nbsp;</mtext></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>+</mo><mi>cz</mi><mo>=</mo><mn>0</mn><mtext>&nbsp;have a non trivial solution, then the value of&nbsp;</mtext><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi mathvariant="normal">a</mi></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi mathvariant="normal">b</mi></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi mathvariant="normal">c</mi></mrow></mfrac><mtext>&nbsp;is equal&nbsp;</mtext></math>to

The equations&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>λ</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mi>x</mi><mo>+</mo><mrow><mo>(</mo><mn>3</mn><mi>λ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>y</mi><mo>+</mo><mn>2</mn><mi>λ</mi><mi>z</mi><mo>=</mo><mn>0</mn><mo>,</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>λ</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mi>x</mi><mo>+</mo><mrow><mo>(</mo><mn>4</mn><mi>λ</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><mi>y</mi><mo>+</mo><mrow><mo>(</mo><mi>λ</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mi>z</mi><mo>=</mo><mn>0</mn><mo>,</mo></math>&nbsp; and &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mrow><mo>(</mo><mn>3</mn><mi>λ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>y</mi><mo>+</mo><mn>3</mn><mrow><mo>(</mo><mi>λ</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mi>z</mi><mo>=</mo><mn>0</mn></math>&nbsp;give non – trivial solution for some values of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math>&nbsp; &nbsp;then the ratio&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>:</mo><mi>y</mi><mo>:</mo><mi>z</mi></math>&nbsp;is -----( when&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math>&nbsp; has smallest of these values)

Which one of the following statements is wrong?

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