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Solve the following system of equations using Cramers rule. `5x-7y+z=11 , 6x-8y-z=15 and 3x+2y-6z=7`

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To solve the system of equations using Cramer's rule, we will follow these steps: Given equations: 1. \( 5x - 7y + z = 11 \) (Equation 1) 2. \( 6x - 8y - z = 15 \) (Equation 2) 3. \( 3x + 2y - 6z = 7 \) (Equation 3) ### Step 1: Write the system in standard form ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Let f(x)=|[cosx , x , x] , [2sinx , x , 2x] , [sinx , x , x]|, then ...

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  2. A triangle has its three sides equal to a , b and c . If the coordin...

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  3. Solve the following system of equations using Cramers rule. 5x-7y+z=1...

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  4. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

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  5. Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(...

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  6. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

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  7. |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A)...

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  8. Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+...

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  9. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

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  10. If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(...

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  11. Find the equation of the line joining A(1,3)a n dB(0,0) using determin...

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  12. If A(x1, y1),B(x2, y2) and C(x3,y3) are vertices of an equilateral ...

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  13. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

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  14. Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[...

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  15. Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x,...

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  16. Without expanding, show that the value of each of the determinants is ...

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  17. Without expanding, show that the value of the determinant is zero: ...

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  18. Without expanding, show that the value of each of the determinants is ...

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  19. Without expanding, show that the value of each of the determinants is ...

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  20. Using the properties of determinants, prove that following |(a-b,-c^2,...

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