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Choose the correct answer If x, y, z ar...

Choose the correct answer
If x, y, z are nonzero real numbers then the inverse of matrix `A=[{:(x,0,0),(0,y,0),(0,0,z):}]`is :

A

`[{:(x^(-1),0,0),(0,y^(-1),0),(0,0,z^(-1)):}]`

B

`xyz[{:(x^(-1),0,0),(0,y^(-1),0),(0,0,z^(-1)):}]`

C

`(1)/(xyz)[{:(x^(-1),0,0),(0,y^(-1),0),(0,0,z^(-1)):}]`

D

`(1)/(xyz)[{:(1,0,0),(0,1,0),(0,0,1):}]`

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Choose the correct answer in questions 17 to 19: If x, y, z are nonzero real numbers then the inverse of metrix A=[{:(x,0,0),(0,y,0),(0,0,z):}] is : (a) [{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}] (b) xyz[{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}] ( c) 1/(xyz)[{:(x,0,0),(0,y,0),(0,0,z):}] (d) 1/(xyz)[{:(1,0,0),(0,1,0),(0,0,1):}]

If x, y, z are non-zero real numbers, then the inverse of matrix A=[(x,0, 0) ,(0,y,0),( 0, 0,z)] is (A) [[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (B) xyz[[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (C) (1)/(xyz)[[x,0,0],[0,y,0],[0,0,z]]] (D) (1)/(xyz)[[1,0,0],[0,1,0],[0,0,1]]

The inverse of the matrix [[x, 0, 0], [0, y, 0], [0, 0, z]] is

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix A=[x0 0 0y0 0 0z] , is [x^(-1)0 0 0y^(-1)0 0 0z^(-1)] (b) x y z[x^(-1)0 0 0y^(-1)0 0 0z^(-1)] (c) 1/(x y z)[x0 0 0y0 0 0z] (d) 1/(x y z)[1 0 0 0 1 0 0 0 1]

The characteristic roots of the matrix [(a,0,0),(x,b,0),(y,z,c)] are

6.If A=[[x,0,0],[0,y,0],[0,0,z]] then A^(-1) is

If A = [(x,0,0),(0,y,0),(0,0,z)] is a non-singular matrix, then find A^(-1) by using elementary row transformations. Hence, write the inverse of [(2,0,0),(0,1,0),(0,0,-1)]

Find the values of x,y,z if the matrix A=[(0,3y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .

MODERN PUBLICATION-DETERMINANTS-OBJECTIVE TYPE QUESTIONS (Multiple choice question)
  1. Let A be a non-singular square matrix of order 3 xx3. Then |adj A| is ...

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  2. If A is an invertible matrix of order 2, then det (A^(-1))is equal to...

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  3. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

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  4. Choose the correct answer If x, y, z are nonzero real numbers then th...

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  5. Let A=[(1,sintheta, 1),(-sintheta, 1, sintheta),(-1, -sintheta, 1)], w...

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  6. If |(2x,5),(8,x)|=|(6,-2),(7,3)| then the value of x is

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  7. Let Delta(1)=|{:(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1):}| and Delta(2)...

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  8. If x , y in R , then the determinant =|cosx-sinx1sinxcosx1cos(x+y)-si...

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  9. If the area of a triangle with vertices (-3,0),(3,0) and (0,0 is 9 sq....

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  10. If A,B and C are angles of a triangle then the determinant |(-1,cosC...

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  11. If A is a sqaure matrix of order 3xx3 and |A|=5, then |adj.A| is

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  12. The value of 'x' for which |{:(3,x),(x,1):}|=|{:(3,2),(4,1):}| is

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  13. Evalute the determinants in queations 1 and 2 : If |{:(x,2),(18,x):}...

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  14. If A is a matrix of order 3xx3 and |A|=10 , then |adj.A| is

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  15. If A is an invertible matrix of order 2, then det (A^(-1))is equal to...

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  16. If |{:(2,3-x),(1,4):}|=0, then value of 'x' is

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  17. If |{:(x,12),(3,x):}|=|{:(6,18),(2,6):}|, then value of 'x' is

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  18. Let A be a non-singular square matrix of order 3 xx3. Then |adj A| is ...

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  19. If A and B are invertible matrices of the same order, then (AB)' is eq...

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  20. If determinant A is order 2xx2 and |A|=3, then the value of |2A| is

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