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By using properties of determinants. Sho...

By using properties of determinants. Show that:
(i) `|(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2`
(ii) `|(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)`

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To solve the given determinants using properties of determinants, we will break down each part step by step. ### Part (i) We need to show that: \[ |(x+4, 2x, 2x), (2x, x+4, 2x), (2x, 2x, x+4)| = (5x-4)(4-x)^2 \] ...
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NCERT ENGLISH-DETERMINANTS-All Questions
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  2. Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2x y...

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  3. Use product [1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2] to solve th...

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  4. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

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  5. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x...

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  6. By using properties of determinants. Show that: (i) |[a-b-c,2a,2a],[2b...

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  7. By using properties of determinants. Show that:|[1,x,x^2],[x^2, 1,x],[...

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  8. By using properties of determinants. Show that:|[1+a^2-b^2, 2a b,-2b],...

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  9. By using properties of determinants. Show that:|[a^2+1,a b, a c],[ a b...

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  10. Let A be a square matrix of order 3xx3, then |k A|is equal to (A) k|A...

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  11. Which of the following is correct (A)   Determinant is a square matrix...

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  12. Solve system of linear equations, using matrix method, 4x - 3y = 3" "...

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  13. Solve system of linear equations, using matrix method, 2x - y = -2" "...

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  14. Examine the consistency of the system of equations x + 3 y = 5" "2x + ...

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  15. Examine the consistency of the system of equations 2x - y = 5" "x + y ...

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  16. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost o...

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  17. Prove that the determinant [(x,sintheta,costheta),(-sintheta,-x,1),(co...

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  18. Find the inverse the matrix (if it exists)given in[(1,-1, 2),( 0, 2,-3...

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  19. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

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  20. If A=[(3, 1),( 1, 2)], show that A^2-5A+5I=0. Hence, find A^(-1).

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