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Mathematics

If [x1][1020]=0\begin{bmatrix} x & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \ -2 & 0 \end{bmatrix} = 0, then the value of x is :

  1. 0

  2. 1

  3. 2

  4. -2

Matrices

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Answer

Given,

[x1][1020]=0\begin{bmatrix} x & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \ -2 & 0 \end{bmatrix} = 0

Solving,

[x(1)+(1)(2)(x)(0)+(1)(0)]=0[x20]=[00]\Rightarrow \begin{bmatrix} x(1) + (1)(-2) & (x)(0) + (1)(0) \end{bmatrix} = 0 \\[1em] \Rightarrow \begin{bmatrix} x - 2 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \end{bmatrix}

∴ x - 2 = 0

⇒ x = 2

Hence, option 3 is the correct option.

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