text If A- begin bmatrix 3 -1 14 -1lendbmatrix - text and -A -10- beginbmatrix a -11- a -12 1a -21- a 22lendbmatrix - 11 then - a-11-a-22-

A=[ 3 amp; 1; 4 amp; 1 nbsp; ]= [ 1 amp; 0; 0 amp; 1 nbsp; ]+ [ 2 amp; 1; 4 amp; 2 nbsp; nbsp; ] ...

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Adjoint of a Matrix

text If A= be...

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

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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} =

3 \times 3

M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦, a n d M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦ .

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

where (a \neq \frac{11}{3})

d e t . (adj(adj A)) = (23)^{4},

a

Find a and b if
$a [\begin{matrix} 17 \end{matrix}] - [\begin{matrix} 3 b \end{matrix}] = [\begin{matrix} 224 \end{matrix}]$

[\begin{matrix} - 3 & 2 5 & - 1 \end{matrix}]

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