Let \(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) and \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\), such that A= B, then the value of α is:

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  1. -1
  2. 1
  3. 2
  4. -2

Answer (Detailed Solution Below)

Option 3 : 2
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Given:

\(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) and \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\)  such that A= 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  A= 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.

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