AP EAMCET · Maths · Matrices
If \(A=\left[\begin{array}{cccc}2 & 1 & 3 & -1 \\ 1 & -2 & 2 & -3\end{array}\right], B=\left[\begin{array}{cccc}2 & 1 & 0 & 3 \\ 1 & -1 & 2 & 3\end{array}\right]\) and \(2 \mathrm{~A}+3 \mathrm{~B}-5 \mathrm{C}=0\), then \(\mathrm{C}=\)
- A \(\left[\begin{array}{cccc}2 & 1 & 6 / 5 & 7 / 5 \\ 1 & 7 / 5 & 2 & 3 / 5\end{array}\right]\)
- B \(\left[\begin{array}{cccc}-2 & 1 & 6 / 5 & 7 / 5 \\ 1 & -7 / 5 & 2 & 3 / 5\end{array}\right]\)
- C \(\left[\begin{array}{cccc}-2 & 1 & 6 / 5 & 7 / 5 \\ 1 & 7 / 5 & 2 & 3 / 5\end{array}\right]\)
- D \(\left[\begin{array}{cccc}2 & 1 & 6 / 5 & 7 / 5 \\ 1 & -7 / 5 & 2 & 3 / 5\end{array}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[\begin{array}{cccc}2 & 1 & 6 / 5 & 7 / 5 \\ 1 & -7 / 5 & 2 & 3 / 5\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Since } 2 \mathrm{~A}+3 \mathrm{~B}-5 \mathrm{C}=0 \\ & \Rightarrow 5 \mathrm{C}=2 \mathrm{~A}+3 \mathrm{~B} \\ & \Rightarrow 5 \mathrm{C}=2\left[\begin{array}{llll}2 & 1 & 3 & -1 \\ 1 & -2 & 2 & -3\end{array}\right]+3\left[\begin{array}{llll}2 & 1 & 0…
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