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The inverse of the matrix [(1, 0,0),(a,1...

The inverse of the matrix `[(1, 0,0),(a,1,0),(b,c,1)]` is -

A

`[(1,0,0),(-a,1,0),(ac-b,-c,1)]`

B

`[(1,0,0),(-a,1,0),(-b,-c,1)]`

C

`[(1,-a,ac-b),(0,1,-c),(0,0,1)]`

D

`[(1,0,0),(-a,1,0),(ac,b,1)]`

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A
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Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Similarly, if there exists a matrix R of type nxxm such that AR=I_(m) , then R is called right inverse of A. For example, to find right inverse of matrix A=[(1,-1),(1,1),(2,3)] , we take R=[(x,y,x),(u,v,w)] and solve AR=I_(3) , i.e., [(1,-1),(1,1),(2,3)][(x,y,z),(u,v,w)]=[(1,0,0),(0,1,0),(0,0,1)] {:(implies,x-u=1,y-v=0,z-w=0),(,x+u=0,y+v=1,z+w=0),(,2x+3u=0,2y+3v=0,2z+3w=1):} As this system of equations is inconsistent, we say there is no right inverse for matrix A. The number of right inverses for the matrix [(1,-1,2),(2,-1,1)] is

Find the inverse of matrix: A = [(1,2),(-3,-1)]

Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Similarly, if there exists a matrix R of type nxxm such that AR=I_(m) , then R is called right inverse of A. For example, to find right inverse of matrix A=[(1,-1),(1,1),(2,3)] , we take R=[(x,y,x),(u,v,w)] and solve AR=I_(3) , i.e., [(1,-1),(1,1),(2,3)][(x,y,z),(u,v,w)]=[(1,0,0),(0,1,0),(0,0,1)] {:(implies,x-u=1,y-v=0,z-w=0),(,x+u=0,y+v=1,z+w=0),(,2x+3u=0,2y+3v=0,2z+3w=1):} As this system of equations is inconsistent, we say there is no right inverse for matrix A. For which of the following matrices, the number of left inverses is greater than the number of right inverses ?

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 7
  1. The inverse of the matrix [(1, 0,0),(a,1,0),(b,c,1)] is -

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  2. If A=|a(ij)| and A(ij) denotes the cofactor of a(ij), then which of th...

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  3. The minors of (-4) and 9 and the cofactors of (-4) and 9 in matrix [(...

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  4. If |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 then the value of x is -

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  5. If the system of equations x+y+z=6, x+2y+kz=0 and x+2y+3z=10 has no so...

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  6. If A=[(-i,0),(0,i)] then A^(T)A is equal to -

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  7. If A=[(0,3),(4,5)] and kA=[(0,4a),(3b,60)], then the values of k, a an...

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  8. The value of the determinant |(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)...

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  9. If the matrix A stisfies the equation [(1,3),(0,1)]*A=[(1,1),(0,-1)],...

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  10. For any matrix A, if A^(-1) exists then which of the following is not ...

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  11. If a(1), a(2), a(3)…, a(n) are in G.P., then the value of the determin...

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  12. The value of the determinant |((10)!,(11)!,(12)!),((11)!,(12)!,(13)!),...

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  13. If C is the midpoint of AB and P is any point outside AB, then which o...

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  14. The position vectors of the points A, B, C are (hati-3hatj-5hatk),(2h...

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  15. If N be the set of natural numbers and and N(a)={an :n in N} then N(5)...

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  16. If the function f: R to R is defined by f(x)=x^(2)-6x-14, then f^(-1)(...

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  17. Let f:R to R be defined by f(x)=x^(2) and g:R to R be defined by g(...

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  18. If f:R to S is defined by f(x)=sinx-sqrt(3)cosx+1 is onto, then the in...

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  19. If (x^(3))/((2x-1) (x+2) (x-3))=A+ (B)/(2x-1) +(C )/(x+2) + (D)/(x-3),...

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  20. The value of ["tan"^(-1)(m)/(n)-tan^(-1)((m-n)/(m+n))] is -

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