Question
Download Solution PDFLet \(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) and \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\), such that A2 = B, then the value of α is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) and \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\) such that A2 = B
Concept:
Two matrices are equal when all positional elements are equal for both matrices.
Calculation:
\(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) and \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\)
Then
\(A^2=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\cdot \left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\)
\(A^2=\left(\begin{array}{cc} α^2 & α-1 \\ 0 & 1 \end{array}\right)\)
Given A2 = B then
\(\left(\begin{array}{cc} α^2 & α-1 \\ 0 & 1 \end{array}\right)=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\)
⇒ α2 = 4 and α - 1 = 1
⇒ α = ± 2 and α = 2
Then α = 2
Hence the option (3) is correct.
Last updated on Jun 19, 2025
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