Question
Download Solution PDFयदि \(A = \begin{bmatrix} -1 & 2 & 3 & -2 \\\ 2 & -5 & 1 & 2 \\\ 3 & -8 & 5 & 2 \\\ 5 & -12 & -1 & 6 \end{bmatrix}\) तो आव्यूह A की रैंक क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFR1 → -R1
\(A = \begin{bmatrix} 1 & -2 & -3 & 2 \\\ 2 & -5 & 1 & 2 \\\ 3 & -8 & 5 & 2 \\\ 5 & -12 & -1 & 6 \end{bmatrix}\)
R2 → R2 - 2R1; R3 → R3 - 3R1; R4 → R4 - 5R1
\(= \begin{vmatrix} 1 & -2 & -3 & 2 \\\ 0 & -1 & 7 & -2 \\\ 0 & -2 & 14 & -4 \\\ 0 & -2& 14& -4\end{vmatrix}\)
R4 → R4 - 2R2; R3 → R3 - 2R2
\(= \begin{vmatrix} 1 & -2 & -3 & 2 \\\ 0 & -1 & 7 & -2 \\\ 0 & 0 & 0 & 0 \\\ 0 & 0& 0& 0\end{vmatrix}\)
तो, r[A] = 2
Last updated on Jul 2, 2025
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