in Linear Algebra recategorized by
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Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are the row vecotrs. Consider the Following statements:

Statement $1$: $u_1^Tv_1  = 1$ and $u_2^Tv_2= 1$

 Statement $2$: $u_1^Tv_2  = 0$ and $u_2^Tv_1= 0$

  1. Statement $1$ is True and Statement $2$ is false
  2. Statement $2$ is true and Statement $1$ is false
  3. Both the Statements are true
  4. Both the statements are false
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