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I have this system :

[tex](A_1 \quad A_2 \quad A_3 \;...)\left( {\matrix{

{b_1 } \cr

{b_2 } \cr

{b_3 } \cr

{...} \cr

} } \right) = C[/tex]

where the A's are matrices that forms a vector, b is a vector and C a matrix. If I know C and the A's. How can I find the b's?

[tex]\left( {\matrix{

{b_1 } \cr

{b_2 } \cr

{b_3 } \cr

{...} \cr

} } \right) = (A_1^{ - 1} \quad A_2^{ - 1} \quad A_3^{ - 1} \;...)C

[/tex]

Surely not, this give another matrix. The A's are square but not necessarely invertable...

[tex](A_1 \quad A_2 \quad A_3 \;...)\left( {\matrix{

{b_1 } \cr

{b_2 } \cr

{b_3 } \cr

{...} \cr

} } \right) = C[/tex]

where the A's are matrices that forms a vector, b is a vector and C a matrix. If I know C and the A's. How can I find the b's?

[tex]\left( {\matrix{

{b_1 } \cr

{b_2 } \cr

{b_3 } \cr

{...} \cr

} } \right) = (A_1^{ - 1} \quad A_2^{ - 1} \quad A_3^{ - 1} \;...)C

[/tex]

Surely not, this give another matrix. The A's are square but not necessarely invertable...

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