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Hi

I have a question in my math coursework on matrices

Question is

Three matrices A, B and C are given by:

[tex]A = \begin{pmatrix} 2 & 5 \\ -4 & 1 \end{pmatrix} [/tex]

[tex]B = \begin{pmatrix} 1 & 3 \\ -2 & 6 \end{pmatrix}[/tex]

[tex]C = \begin{pmatrix} 2 & 1 \\ -3 & -1 \end{pmatrix}[/tex]

a) find the inverses of A and B

b) Solve the equation AXB=C

This is my solution

iknow have rearranged equation to make it

[itex]{X=}A\frac{C}{A B} [/itex]

i understand that you can't dived in matrices so i have to use the inverse of A and B

to make the equation [itex]{X=}{A}^{-1} {C} {B}^{-1} [/itex]

The det [itex]\left|A\right|[/itex] = 22

det [itex]\left|B\right|[/itex] = 12

[itex]A^{-1} = \frac{1}{22}[/itex] \begin{pmatrix} 1 & -5 \\ 4 & 2 \end{pmatrix}

[itex]B^{-1} = \frac{1}{12} [/itex] /begin{pmatrix} 6 & -3 \\ 2 & 1 \end{pmatrix}

and my answer for inv A mutliplied C is \frac{1}{22}[/itex] \begin{pmatrix} 17 & 6 \\ 2 & 2 \end{pmatrix} or \begin{pmatrix} 0.7727 & 0.2727 \\ 0.0909 & 0.0909\end{pmatrix}

and then i mutlipy by inv B i get matrix X= \begin{pmatrix} 0.4318 & -0.1705 \\ 0.0606 & -0.0152\end{pmatrix}

my question is this answer correct and how can i show the answer for Matrix X as [itex]X=\frac{1}{?} [/itex]\begin{pmatrix} a & b \\ c & d\end{pmatrix}

do i add the [itex]\frac {1}{22}+ \frac{1}{12} [/itex]which would make it [itex] \frac{1}{34} ??????[/itex]

would this then make Matrix X [itex]X=\frac{1}{34} [/itex]\begin{pmatrix} a & b \\ c & d\end{pmatrix}

I have a question in my math coursework on matrices

Question is

Three matrices A, B and C are given by:

[tex]A = \begin{pmatrix} 2 & 5 \\ -4 & 1 \end{pmatrix} [/tex]

[tex]B = \begin{pmatrix} 1 & 3 \\ -2 & 6 \end{pmatrix}[/tex]

[tex]C = \begin{pmatrix} 2 & 1 \\ -3 & -1 \end{pmatrix}[/tex]

a) find the inverses of A and B

b) Solve the equation AXB=C

This is my solution

iknow have rearranged equation to make it

[itex]{X=}A\frac{C}{A B} [/itex]

i understand that you can't dived in matrices so i have to use the inverse of A and B

to make the equation [itex]{X=}{A}^{-1} {C} {B}^{-1} [/itex]

The det [itex]\left|A\right|[/itex] = 22

det [itex]\left|B\right|[/itex] = 12

[itex]A^{-1} = \frac{1}{22}[/itex] \begin{pmatrix} 1 & -5 \\ 4 & 2 \end{pmatrix}

[itex]B^{-1} = \frac{1}{12} [/itex] /begin{pmatrix} 6 & -3 \\ 2 & 1 \end{pmatrix}

and my answer for inv A mutliplied C is \frac{1}{22}[/itex] \begin{pmatrix} 17 & 6 \\ 2 & 2 \end{pmatrix} or \begin{pmatrix} 0.7727 & 0.2727 \\ 0.0909 & 0.0909\end{pmatrix}

and then i mutlipy by inv B i get matrix X= \begin{pmatrix} 0.4318 & -0.1705 \\ 0.0606 & -0.0152\end{pmatrix}

my question is this answer correct and how can i show the answer for Matrix X as [itex]X=\frac{1}{?} [/itex]\begin{pmatrix} a & b \\ c & d\end{pmatrix}

do i add the [itex]\frac {1}{22}+ \frac{1}{12} [/itex]which would make it [itex] \frac{1}{34} ??????[/itex]

would this then make Matrix X [itex]X=\frac{1}{34} [/itex]\begin{pmatrix} a & b \\ c & d\end{pmatrix}

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