Question
If inverse of $\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right]$ is $\left[\begin{array}{ccc}p & 0 & 0 \\ 0 & q & 0 \\ 0 & 0 & r\end{array}\right]$, then $p a+q b+r c$ is(a) 0(b) 1(c) $(a+b+c)(p+q+r)$(d) 3
Step 1
Step 1: Given a diagonal matrix $\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right]$ and its inverse $\left[\begin{array}{ccc}p & 0 & 0 \\ 0 & q & 0 \\ 0 & 0 & r\end{array}\right]$. Show more…
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$$\text { If } a b c \neq 0, \text { find the inverse of }\left[\begin{array}{lll} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{array}\right]$$
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The Inverse of a Matrix
Inverse of the matrix $\left[\begin{array}{lll}\mathrm{p} & 0 & 0 \\ 0 & \mathrm{q} & 0 \\ 0 & 0 & \mathrm{r}\end{array}\right]$ where pqr $\neq 0$ is (a) $\left[\begin{array}{lll}0 & 0 & \mathrm{p} \\ 0 & \mathrm{q} & 0 \\ \mathrm{r} & 0 & 0\end{array}\right]$ (b) $\left[\begin{array}{lll}\mathrm{p} & 0 & 0 \\ 0 & \mathrm{q} & 0 \\ 0 & 0 & \mathrm{r}\end{array}\right]$ (c) $\left[\begin{array}{ccc}0 & 0 & -\mathrm{p} \\ 0 & -\mathrm{q} & 0 \\ -\mathrm{r} & 0 & 0\end{array}\right]$ (d) $\left[\begin{array}{ccc}p^{-1} & 0 & 0 \\ 0 & q^{-1} & 0 \\ 0 & 0 & r^{-1}\end{array}\right]$
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