If matrix A - begin bmatrix 1 - 0 -13 - 4 - 5 1086 - 7lend bmatrix and its inverse is denoted by A -1- egin bmatrix a 11- a 12- a 13 1a -21- a -22- a -23 1a 31- a-32- a 33end bmatrix - then the value of a 23-A- 21-20B- 1-EC- -2-5D- 2-5

The correct option is D 2/5|A| = 20 ∴ a_23 = Cofactor of 6/ 20 = 8/ 20 = 2/5 ...

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Inverse of a Matrix

If matrix A =...

Question

If matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & - 1 3 & 4 & 5 0 & 6 & 7 \end{matrix} ⎤ ⎥ ⎦$ and its inverse is denoted by $A^{- 1} = ⎡ ⎢ ⎣ \begin{matrix} a_{11} & a_{12} & a_{13} a_{21} & a_{22} & a_{23} a_{31} & a_{32} & a_{33} \end{matrix} ⎤ ⎥ ⎦$ , then the value of $a_{23}$ =

\frac{21}{20}

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\frac{1}{5}

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- \frac{2}{5}

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\frac{2}{5}

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Solution

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A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & - 1 3 & 4 & 5 0 & 6 & 7 \end{matrix} ⎤ ⎥ ⎦

A^{- 1} = ⎡ ⎢ ⎣ \begin{matrix} a_{11} & a_{12} & a_{13} a_{21} & a_{22} & a_{23} a_{31} & a_{32} & a_{33} \end{matrix} ⎤ ⎥ ⎦

a_{23} =

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 0 2 & 1 & 5 1 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦

a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23} =

If A = [\begin{matrix} 3 & - 1 4 & - 1 \end{matrix}] and A^{10} = [\begin{matrix} a_{11} & a_{12} a_{21} & a_{22} \end{matrix}], then a_{11} + a_{22} =

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 & 1 2 & 1 & - 3 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦

10 B = ⎡ ⎢ ⎣ \begin{matrix} 4 & 2 & 2 - 5 & 0 & α 1 & - 2 & 3 \end{matrix} ⎤ ⎥ ⎦

B

A

α

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 1 & 1 & 5 2 & 4 & 7 \end{matrix} ⎤ ⎥ ⎦

a_{31} A_{31} + a_{32} A_{32} + a_{33} A_{33}

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