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निम्नलिखित में सारणिक का मान निकाले ।...

निम्नलिखित में सारणिक का मान निकाले ।
(i) `|{:(5,-10),(0,3):}|` (ii) `|{:(1,0,4),(3,5,-1),(0,1,2):}|` (III)`|{:(1,0,0),(0,1,0),(0,0,1):}|`

लिखित उत्तर

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(i) `M_(11)=3," "M_(12)=0" "M_(21)=-10" "M_(22)=5,`
`A_(11)=3," "A_(12)=0," "A_(21)=10" "A_(22)=5," "Delta=15`
(ii) `M_(11)=11," "M_(12)=6," "M_(13)=3," "M_(21)=-4," "M_(22)=2`
`M_(23)=1," "M_(31)=-20," "M_(32)=-13" "M_(33)=5,`
`A_(11)=11," "A_(12)=-6," "A_(13)=3," "A_(21)=4," "A_(22)=2`
`A_(23)=-1," "A_(31)=-20" "A_(32)=13," "a_(33)=5," "Delta=23`
(iii) `M_(11)=-40," "M_(12)=-10," "M_(13)=35," "M_(21)=16,`
`M_(22)=8," "M_(23)=-4," "M_(31)=8," "M_(32)=14," "M_(33)=-17`
`A_(11)=-40," "A_(12)=10," "A_(13)=35," "A_(21)=-16`,
`A_(22)=8," "A_(23)=4," "A_(31)=8," "A_(32)=-14`,
`A_(33)=-17,Delta=-80`
(iv) `M_(11)=1," "M_(12)=0," "M_(13)=0," "M_(21)=0," "M_(22)=1`
`M_(23)=0," "M_(31)=0," "M_(32)=0," "M_(33)=1,`
`A_(11)=1," "A_(12)=0," "A_(13)=0," "A_(21)=0," "A_(22)=1`,
`A_(23)=0," "A_(31)=0," "A_(32)=0," "A_(33)=1," "Delta=1`
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KC SINHA-सारणिक -अभ्यास 6.1
  1. निम्नलिखित का मान निकाले (i) |{:(7,5),(-2,3):}| (ii) |{:(cosalpha,si...

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  2. निम्नलिखित सारणिकों में दूसरे स्तम्भ के प्रत्येक अवयव का उपसारणिक तथा ...

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  3. निम्नलिखित में सारणिक का मान निकाले । (i) |{:(5,-10),(0,3):}| (ii...

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  4. निम्नलिखित का मान निकाले |{:(1,5,7),(6,7,2),(1,2,3):}|

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  5. निम्नलिखित का मान निकाले |{:(1,1,1),(1,1+x,1),(1,1,1+y):}|

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  6. निम्नलिखित का मान निकाले |{:(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2...

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  7. साबित करे कि |{:(x,y,z),(x^(2),y^(2),z^(2)),(yz,zx,xy):}|=(y-z)(z-x)(x...

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  8. साबित करे कि |{:(1,a^(2)+bc,a^(3)),(1,b^(2)+ca,b^(3)),(1,c^(2)+ab,c^...

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  9. सारणिक के गुणों का प्रयोग कर साबित करे । (i) |{:(x+y,x,x),(5x+4y,4x,...

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  10. (i) यदि x,y,z असमान हो तथा Delta=|{:(x,x^(2),1+x^(2)),(y,y^(2),1+y^(...

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  11. साबित करे कि |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)...

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  12. साबित करे कि |{:(a+b+c,-c,-b),(-c,a+b+c,-a),(-b,-a,a+b+c):}|=2(a+b)(...

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  13. (i) साबित करे कि |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2) ...

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  14. साबित करे कि |{:(1,x,x^(2)),(x^(2),1,x),(x,x^(2),1):}|=(1-x^(3))^(2)

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  15. साबित करे कि |{:(a,b-c,c+b),(a+c,b,c-a),(a-b,a+b,c):}|=(a+b+c)(a^(2)...

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  16. साबित करे कि |{:((b+c)^(2),a^(2),bc),((c+a)^(2),b^(2),ca),((a+b)^(2)...

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  17. साबित करे कि |{:(a^(2),a^(2)-(b-c)^(2),bc),(b^(2),b^(2)-(c-a)^(2),ca...

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  18. साबित करे कि |{:(b^(2)+c^(2),a^(2),a^(2)),(b^(2),c^(2)+a^(2),b^(2)),...

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  19. साबित करे कि |{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^(2)-ac...

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  20. साबित करे कि |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-...

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