Find the matrix X in the equation AX-B- such that A- 1 3 0 1 - and B- 1 -1 0 1 -

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Find the matr...

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Find the matrix X in the equation AX=B, such that A=\begin{bmatrix}1&3 0&1\end{bmatrix} and B=\begin{bmatrix}1&-1 0&1\end{bmatrix}

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α

⎡ ⎢ ⎣ \begin{matrix} 1 & α & α^{2} α & 1 & α α^{2} & α & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 1 \end{matrix} ⎤ ⎥ ⎦

1 + α + α^{2} =

X_{1}

X_{2}

X_{3}

A x = b

b

b_{1}

b_{2}

b_{3}

X_{1} = ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦, X_{2} = ⎡ ⎢ ⎣ \begin{matrix} 021 \end{matrix} ⎤ ⎥ ⎦, X_{3} = ⎡ ⎢ ⎣ \begin{matrix} 001 \end{matrix} ⎤ ⎥ ⎦, b_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, b_{2} = ⎡ ⎢ ⎣ \begin{matrix} 020 \end{matrix} ⎤ ⎥ ⎦

b_{3} = ⎡ ⎢ ⎣ \begin{matrix} 002 \end{matrix} ⎤ ⎥ ⎦

A

For the matrix $A = [\begin{matrix} 3 & 2 1 & 1 \end{matrix}]$ , find the numbers a and b such that $A^{1} + a A + b I = 0$

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦

u_{1}

u_{2}

A u_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦

A u_{2} = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦

u_{1} + u_{2}

If $A = d i a g [35] a n d B = d i a g [2 - 3]$ , find A + 2B :

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