Question #211529

Let B=(1023)B = \begin{pmatrix} 1 & 0 \\ 2 & 3 \end{pmatrix}

What is B-1?

1
Expert's answer
2021-07-01T16:10:38-0400

Given (1023)\begin{pmatrix} 1& 0 \\ 2 & 3 \end{pmatrix}

A=(abcd)A=\begin{pmatrix} a & b \\ c & d \end{pmatrix}

A1=1adbc(dbca)A^{-1}=\frac{1}{ad-bc}\begin{pmatrix} d &- b \\ - c & a \end{pmatrix}

B1=11×32×0(3021)B^{-1}=\frac{1}{1×3-2×0}\begin{pmatrix} 3 & 0 \\ -2 & 1 \end{pmatrix}


B1=13(3021)B^{-1}=\frac{1}{3}\begin{pmatrix} 3 & 0\\ -2 & 1 \end{pmatrix}


B1=(102313)B^{-1}=\begin{pmatrix} 1 & 0 \\ \frac{-2}{3} & \frac{1}{3} \end{pmatrix}

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