Dr.Harswaroop Sharma Mathematics Solution Class 12 Chapter 3 आव्यूह (Matrices) Exercise 3D

      

प्रश्नावली - 3D

निम्नलिखित आव्यूहों के व्युत्क्रम, यदि उनका अस्तित्व है, तो प्रारन्भिक रुपान्तरण के प्रयोग से ज्ञात कीजिए :

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Question 1

1. $\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right]$

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Question 2

2. $\left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right]$

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Question 3

3. $\left[\begin{array}{ll}1 & 3 \\ 2 & 7\end{array}\right]$

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Question 4

4. $\left[\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right]$

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Question 5

5. $\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$

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Question 6

6. $\left[\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right]$

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Question 7

7. $\left[\begin{array}{ll}3 & 1 \\ 5 & 2\end{array}\right]$

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Question 8

8. $\left[\begin{array}{ll}4 & 5 \\ 3 & 4\end{array}\right]$

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Question 9

9. $\left[\begin{array}{cc}3 & 10 \\ 2 & 7\end{array}\right]$

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Question 10

10. $\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$

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Question 11

11. $\left[\begin{array}{ll}2 & -6 \\ 1 & -2\end{array}\right]$

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Question 12

12. $\left[\begin{array}{cc}6 & -3 \\ -2 & 1\end{array}\right]$

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Question 13

13. $\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$

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Question 14

14. $\left[\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right]$

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Question 15

15. यदि $A$ तथा $B$ एक ही क्रम के व्युत्क्रमणीय वर्ग आव्यूह हों, तो सिद्ध कीजिए कि $(A B)^{-1}=B^{-1} A^{-1}$.

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Question 16

16. यदि $A=\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right]$, तो $A^{-1}$ ज्ञात कीजिए।

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Question 17

17. यदि $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2\end{array}\right]$, तो $A$ का व्युत्क्रम आव्यूह ज्ञात कीजिए।

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Question 18

18. आव्यूह $\left[\begin{array}{rrr}1 & 2 & 1 \\ 1 & -1 & -2 \\ 1 & 2 & -1\end{array}\right]$ के परिवर्त [transpose] का प्रतिलोम ज्ञात कीजिए।

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Question 19

19. $\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$

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Question 20

20. $\left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$

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Question 21

21. सिद्ध कीजिए कि $\left[\begin{array}{rrr}1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & -6 & -7\end{array}\right]^{-1}=\frac{1}{20}\left[\begin{array}{rrr}2 & 6 & 4 \\ 21 & -7 & -8 \\ -18 & 6 & 4\end{array}\right]$.

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Question 22

22. यदि $A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right]$ है, तो सिद्ध कीजिए कि $A^3=A^{-1}$.