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Find the transpose \(A^T\) of \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\).\(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) का transpose \(A^T\) ज्ञात कीजिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\begin{bmatrix}1&3\\2&4\end{bmatrix}\)\(\begin{bmatrix}1&3\\2&4\end{bmatrix}\)
Transpose means rows become columns. So the entry at position \((1,2)\) becomes \((2,1)\), etc. For \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\), we get \(A^T=\begin{bmatrix}1&3\\2&4\end{bmatrix}\).Transpose में पंक्तियाँ (rows) स्तम्भ (columns) बन जाती हैं। इसलिए \((1,2)\) पर स्थित प्रविष्टि \((2,1)\) पर आ जाती है, आदि। \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) के लिए \(A^T=\begin{bmatrix}1&3\\2&4\end{bmatrix}\) होगा।
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