सारणिक left|begin{array}{ccc}2 & -3 & 5 6 & | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) उपसारणिक $(M_{ij})$ और सहखंड $(A_{ij})$ की गणना इस प्रकार की जाती है:$M_{11} = \left|\begin{array}{cc}0 & 4 \ 5 & -7\end{array}ight| = 0 - 20 =

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) उपसारणिक $(M_{ij})$ और सहखंड $(A_{ij})$ की गणना इस प्रकार की जाती है:$M_{11} = \left|\begin{array}{cc}0 & 4 \ 5 & -7\end{array}ight| = 0 - 20 = -20; \quad A_{11} = (-1)^{1+1}(-20) = -20$$M_{12} = \left|\begin{array}{cc}6 & 4 \ 1 & -7\end{array}ight| = -42 - 4 = -46; \quad A_{12} = (-1)^{1+2}(-46) = 46$$M_{13} = \left|\begin{array}{cc}6 & 0 \ 1 & 5\end{array}ight| = 30 - 0 = 30; \quad A_{13} = (-1)^{1+3}(30) = 30$$M_{21} = \left|\begin{array}{cc}-3 & 5 \ 5 & -7\end{array}ight| = 21 - 25 = -4; \quad A_{21} = (-1)^{2+1}(-4) = 4$$M_{22} = \left|\begin{array}{cc}2 & 5 \ 1 & -7\end{array}ight| = -14 - 5 = -19; \quad A_{22} = (-1)^{2+2}(-19) = -19$$M_{23} = \left|\begin{array}{cc}2 & -3 \ 1 & 5\end{array}ight| = 10 + 3 = 13; \quad A_{23} = (-1)^{2+3}(13) = -13$$M_{31} = \left|\begin{array}{cc}-3 & 5 \ 0 & 4\end{array}ight| = -12 - 0 = -12; \quad A_{31} = (-1)^{3+1}(-12) = -12$$M_{32} = \left|\begin{array}{cc}2 & 5 \ 6 & 4\end{array}ight| = 8 - 30 = -22; \quad A_{32} = (-1)^{3+2}(-22) = 22$$M_{33} = \left|\begin{array}{cc}2 & -3 \ 6 & 0\end{array}ight| = 0 + 18 = 18; \quad A_{33} = (-1)^{3+3}(18) = 18$यहाँ $a_{11}=2, a_{12}=-3, a_{13}=5$ और $A_{31}=-12, A_{32}=22, A_{33}=18$ है,अतः:$a_{11} A_{31}+a_{12} A_{32}+a_{13} A_{33} = 2(-12) + (-3)(22) + 5(18) = -24 - 66 + 90 = -90 + 90 = 0$.

Similar Questions

सारणिक $\Delta = \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ में अवयव $6$ का उपसारणिक (minor) ज्ञात कीजिए।

आव्यूह $A = \begin{bmatrix} 2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2 \end{bmatrix}$ के प्रथम स्तंभ के अवयवों के सहखंड (cofactors) ज्ञात कीजिए।

दूसरी पंक्ति के अवयवों के सहखंडों (cofactors) का उपयोग करके $\Delta = \left|\begin{array}{lll}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{array}\right|$ का मान ज्ञात कीजिए।

आव्यूह $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$ के लिए,सहखंडज आव्यूह (matrix of cofactors) ज्ञात कीजिए।

Vedclass Test Series

Exam Paper Generator

Online Exam Module