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શ્રેણિક

જો $bold A bold space bold equals bold space open square brackets table row bold 2 cell bold minus bold 4 end cell row bold 3 bold 2 row cell bold minus bold 1 end cell bold 1 end table close square brackets bold space bold અન ે bold space bold B bold space bold equals bold space open square brackets table row cell bold minus bold 3 end cell bold 1 row bold 0 bold 5 row bold 4 cell bold minus bold 2 end cell end table close square brackets$ ,તો A + B, A – B, 2A + B, A – 2B શોધો.

જો $bold A bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta end cell row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets$ , તો A + A^T અને A - A^T શોધો.

અહીં, $bold A bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta end cell row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets$

$bold therefore bold space bold A to the power of bold T bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold cos bold space bold theta end cell row cell bold minus bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets bold A bold space bold plus bold space bold A to the power of bold T bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta end cell row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets bold space bold plus bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold cos bold space bold theta end cell row cell bold minus bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta bold space bold plus bold space bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta bold space bold plus bold space bold cos bold space bold theta end cell row cell bold cos bold space bold theta bold space bold minus bold space bold cos bold space bold theta end cell cell bold sin bold space bold theta bold space bold plus bold space bold sin bold space bold theta end cell end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row cell bold 2 bold space bold sin bold space bold theta end cell bold 0 row bold 0 cell bold 2 bold space bold sin bold space bold theta end cell end table close square brackets bold A bold space bold minus bold space bold A to the power of bold T bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta end cell row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets bold space bold plus bold space open parentheses bold minus bold 1 close parentheses bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold cos bold space bold theta end cell row cell bold minus bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta end cell row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell end table close square brackets bold space bold plus bold space open square brackets table row cell bold minus bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta end cell row cell bold cos bold space bold theta end cell cell bold minus bold sin bold space bold theta end cell end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row cell bold sin bold space bold theta bold space bold minus bold space bold sin bold space bold theta end cell cell bold minus bold cos bold space bold theta bold space bold minus bold space bold cos bold space bold theta end cell row cell bold cos bold space bold theta bold space bold plus bold space bold cos bold space bold theta end cell cell bold sin bold space bold theta bold space bold minus bold space bold sin bold space bold theta end cell end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row bold 0 cell bold minus bold 2 bold space bold cos bold space bold theta end cell row cell bold 2 bold space bold cos bold space bold theta end cell bold 0 end table close square brackets$

જો A = diag [1 -1 2] અને B = diag [3 2 1], B – A, 2A + 3B શોધો.

શ્રેણીક સમીકરણ $open square brackets table row cell bold x to the power of bold 2 end cell row cell bold y to the power of bold 2 end cell end table close square brackets bold space bold minus bold space bold 4 bold space open square brackets table row cell bold 2 bold x end cell row bold y end table close square brackets bold space bold equals bold space open square brackets table row cell bold minus bold 7 end cell row bold 12 end table close square brackets$ નો ઉકેલ મેળવો.

જો $bold a subscript bold ij bold space bold equals bold space open parentheses bold i bold space bold minus bold space bold 2 bold j close parentheses to the power of bold 2 over bold 3 bold comma bold space bold ત ો bold space open square brackets bold a subscript bold ij close square brackets subscript bold 2 bold cross times bold 2 end subscript$ મેળવો.

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