Multiple choice

The following system of equations $$x_1 + x_2 + 2x_3 = 1$$ $$x_1 + 2x_2 + 3x_3 = 2$$ $$x_1 + 4x_2 + αx_3 = 4$$ has a unique solution. The only possible value(s) for α is/are

  1. 0

  2. either 0 or 1

  3. one of 0, 1 or -1

  4. any real number
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

One of 0, 1 or -1, the system will have unique solution. If det A $\ne$0, where A = det A $\ne$ 0 $\Rightarrow$$\alpha$-5 $\ne$0 Since, $\alpha$-5 $\ne$5 Hence $\alpha$ could be any real number except 5.

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