Question
Download Solution PDFमाना \(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) और \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\), जैसे कि A2 = B, तो α का मान है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) और \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\) जैसे कि A2 = B
संकल्पना:
दो आव्यूह तब समान होते हैं जब दोनों आव्यूहों के लिए सभी स्थितीय अवयव समान होते हैं।
गणना:
\(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) और \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\)
तब
\(A^2=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\cdot \left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\)
\(A^2=\left(\begin{array}{cc} α^2 & α-1 \\ 0 & 1 \end{array}\right)\)
दिया गया है A2 = B तब
\(\left(\begin{array}{cc} α^2 & α-1 \\ 0 & 1 \end{array}\right)=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\)
⇒ α2 = 4 और α - 1 = 1
⇒ α = ± 2 और α = 2
तब α = 2
अतः विकल्प (3) सही है।
Last updated on May 26, 2025
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