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The multiplicative inverse of matrix [(...

The multiplicative inverse of matrix `[(2,1),(7,4)]` is -

A

`[(4,-1),(-7,-2)]`

B

`[(4,-1),(-7,2)]`

C

`[(4,-7),(7,2)]`

D

`[(-4,-1),(7,-2)]`

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The correct Answer is:
B
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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

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 7
  1. The multiplicative inverse of matrix [(2,1),(7,4)] is -

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

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

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

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  5. 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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  6. 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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  7. If A=[(-i,0),(0,i)] then A^(T)A is equal to -

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

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

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

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

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

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

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

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

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

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

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

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

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

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