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If |[x-2,-3],[3x,2x]|=3 find the value o...

If `|[x-2,-3],[3x,2x]|=3` find the value of x

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To solve the determinant equation \(|[x-2, -3], [3x, 2x]| = 3\), we will follow these steps: ### Step 1: Write the determinant The determinant of a 2x2 matrix \(|[a, b], [c, d]|\) is calculated as \(ad - bc\). For our matrix, we have: \[ |[x-2, -3], [3x, 2x]| = (x-2)(2x) - (-3)(3x) \] ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If [] denotes the greatest integer less than or equal to the real numb...

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  2. L e t|3y x1|=|3 2 4 1| . Find possible values of xa n dy are natural n...

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  3. If |[x-2,-3],[3x,2x]|=3 find the value of x

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

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  5. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

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  6. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by two methods

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  7. If A=[1 3 2 1] , find the determinant of the matrix A^2-2Adot

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  8. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 1x-...

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  9. The value of the determinant |xx+y x+2y x+2y xx+y x+y x+2y x|i s 9x^2...

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  10. Let f(x)=|[cosx , x , x] , [2sinx , x , 2x] , [sinx , x , x]|, then ...

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

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

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

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

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

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

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

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

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