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Consider a matrix $M=\left[\begin{array}{lll}3 & 4 & 0 \\ 2 & 1 & 0 \\ 3 & 1 & k\end{array}\right]$ and the following
statements
Statement $\mathbf{A}:$ Inverse of $\mathrm{M}$ exists.
Statement $\mathbf{B}: k \neq 0$ Which one of the following in respect of the above matrix and statement is correct?
Options:
statements
Statement $\mathbf{A}:$ Inverse of $\mathrm{M}$ exists.
Statement $\mathbf{B}: k \neq 0$ Which one of the following in respect of the above matrix and statement is correct?
Solution:
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Verified Answer
The correct answer is:
A implies B as well as B implies A
Given $M=\left[\begin{array}{lll}3 & 4 & 0 \\ 2 & 1 & 0 \\ 3 & 1 & k\end{array}\right]$
Now $|M|=\left|\begin{array}{lll}3 & 4 & 0 \\ 2 & 1 & 0 \\ 3 & 1 & k\end{array}\right|=k(3-8)=-5 k$
From statement II, $k \neq 0$ then inverse of $\mathrm{M}$ exist (statement I). Thus, statement Aimplies B as well as B implies A.
Now $|M|=\left|\begin{array}{lll}3 & 4 & 0 \\ 2 & 1 & 0 \\ 3 & 1 & k\end{array}\right|=k(3-8)=-5 k$
From statement II, $k \neq 0$ then inverse of $\mathrm{M}$ exist (statement I). Thus, statement Aimplies B as well as B implies A.
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