Find the matrix A A \(\begin {bmatrix} 0 & 1\\2 & -1 \end {bmatrix}\) = \(\begin…

Explanation

Let A = \(\begin {bmatrix} a & b\\ c & d \end {bmatrix}\)

i.e \(\begin{bmatrix} a & b\\c & d \end{bmatrix}\) \(\begin{bmatrix} 0 & 1\\2 & -1 \end{bmatrix}\) = \(\begin{bmatrix} 2 & -1\\1 & 0 \end{bmatrix}\)

\(\implies \begin {bmatrix} a(0) + b(2) & a(1) + b(-1)\\ c(0) + d(2) & c(1) + d(-1)\end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\ 1 & 0 \end {bmatrix}\)

\(\implies \begin {bmatrix} 2b & a - b\\2d & c - d\end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\ 1 & 0 \end {bmatrix}\)

By comparing

2b = 2

a - b = -1

2d = 1 and

c - d = 0

∴ b = \(^2/_2\) = 1

a - b = -1

⇒ a - 1 = -1

∴ a = 0

∴ d = \(^1/_2\)

⇒ c = d

∴ c = \(^1/_2\)

∴The matrice A = \(\begin {bmatrix} 0 & 1\\^1/_2 & ^1/_2 \end {bmatrix}\)

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