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Solving matrices

Can someone please work me throDSC_6280.jpgugh this since it skips steps thank you!
Original post by PhysicsGal
Can someone please work me through this since it skips steps thank you!


Kinda hard to see since it's so zoomed out; but when it comes to multiplying matrices:

[abcd][ef]=[ae+bfce+df]\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e \\ f \end{bmatrix} = \begin{bmatrix} {ae+bf} \\ {ce+df} \end{bmatrix}

and

[abcd][efgh]=[ae+bgaf+bhce+dgcf+dh]\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e & f \\ g & h \end{bmatrix} = \begin{bmatrix} {ae+bg} & {af+bh} \\ {ce+dg} & {cf+dh} \end{bmatrix}
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PhysicsGal
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Original post by RDKGames
Kinda hard to see since it's so zoomed out; but when it comes to multiplying matrices:

[abcd][ef]=[ae+bfce+df]\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e \\ f \end{bmatrix} = \begin{bmatrix} {ae+bf} \\ {ce+df} \end{bmatrix}
and

[abcd][efgh]=[ae+bgaf+bhce+dgcf+dh]\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e & f \\ g & h \end{bmatrix} = \begin{bmatrix} {ae+bg} & {af+bh} \\ {ce+dg} & {cf+dh} \end{bmatrix}


Thank you! However, its asking to solve for what a and b are with eigenvalues of 0.5 for spin up and -0.5 for spin down. It turns out its about solving eigenvectors, so I have found a youtube video buy cheers!

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