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શ્રેણિક

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.

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.

bold A bold space bold plus bold space bold B 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 plus 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 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 minus bold space bold 3 end cell cell bold minus bold 4 bold space bold plus bold space bold 1 end cell row cell bold 3 bold space bold plus bold space bold 0 end cell cell bold 2 bold space bold plus bold space bold 5 end cell row cell bold minus bold 1 bold space bold plus bold space bold 4 end cell cell bold 1 bold space bold minus bold space bold 2 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 equals bold space open square brackets table row cell bold minus bold 1 end cell cell bold minus bold 3 end cell row bold 3 bold 7 row bold 3 cell bold minus bold 1 end cell end table close square brackets bold A bold space bold minus bold space bold B bold space bold equals bold space bold A bold space bold plus bold space bold left parenthesis bold minus bold B bold right parenthesis 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 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 plus bold space open square brackets table row bold 3 cell bold minus bold 1 end cell row bold 0 cell bold minus bold 5 end cell row cell bold minus bold 4 end cell bold 2 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 plus bold space bold 3 end cell cell bold minus bold 4 bold space bold minus bold space bold 1 end cell row cell bold 3 bold space bold plus bold space bold 0 end cell cell bold 2 bold space bold minus bold space bold 5 end cell row cell bold minus bold 1 bold space bold minus bold space bold 4 end cell cell bold 1 bold space bold plus bold space bold 2 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 5 cell bold minus bold 5 end cell row bold 3 cell bold minus bold 3 end cell row cell bold minus bold 5 end cell bold 3 end table close square brackets bold 2 bold A bold space bold plus bold space bold B bold space bold equals bold space bold 2 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 plus 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

bold equals bold space open square brackets table row bold 4 cell bold minus bold 8 end cell row bold 6 bold 4 row cell bold minus bold 2 end cell bold 2 end table close square brackets bold space bold plus 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 bold equals bold space open square brackets table row cell bold 4 bold space bold minus bold space bold 3 end cell cell bold minus bold 8 bold space bold plus bold space bold 1 end cell row cell bold 6 bold space bold plus bold space bold 0 end cell cell bold 4 bold space bold plus bold space bold 5 end cell row cell bold minus bold 2 bold space bold plus bold space bold 4 end cell cell bold 2 bold space bold minus bold space bold 2 end cell end table close square brackets bold equals bold space open square brackets table row bold 1 cell bold minus bold 7 end cell row bold 6 bold 9 row bold 2 bold 0 end table close square brackets

bold A bold space bold minus bold space bold 2 bold B bold space bold equals bold space bold A bold space bold plus bold space open parentheses bold minus bold 2 close parentheses bold space bold B

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 plus bold space open parentheses bold minus bold 2 close parentheses 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 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 plus bold space open square brackets table row bold 6 cell bold minus bold 2 end cell row bold 0 cell bold minus bold 10 end cell row cell bold minus bold 8 end cell bold 4 end table close square brackets bold equals bold space open square brackets table row cell bold 2 bold space bold plus bold space bold 6 end cell cell bold minus bold 4 bold space bold minus bold space bold 2 end cell row cell bold 3 bold space bold plus bold space bold 0 end cell cell bold 2 bold space bold minus bold space bold 10 end cell row cell bold minus bold 1 bold space bold minus bold space bold 8 end cell cell bold 1 bold space bold plus bold space bold 4 end cell end table close square brackets bold equals bold space open square brackets table row bold 8 cell bold minus bold 6 end cell row bold 3 cell bold minus bold 8 end cell row cell bold minus bold 9 end cell bold 5 end table close square brackets

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

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.

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