Matrices a and B satisfy `AB=B^(-1)`, where `B=[(2,-1),(2,0)]`. Find (i) without finding `B^(-1)`, the value of K for which `KA-2B^(-1)+I=O`. (ii) without finding `A^(-1)`, the matrix X satifying `A^(-1) XA=B`.

Matrices a and B satisfy `AB=B^(-1)`, where `B=[(2,-1),(2,0)]`. Find (

1.	Matrices a and B satisfy `AB=B^(-1)`, where `B=[(2,-1),(2,0)]`. Find (i) without finding `B^(-1)`, the value of K for which `KA-2B^(-1)+I=O`. (ii) without finding `A^(-1)`, the matrix X satifying `A^(-1) XA=B`.
Answer» (i) `AB=B^(-1)` or `AB B=B^(-1)B` or `AB^(2)=I` Now, `KA-2B^(-1)+I=O` or `KAB-2B^(-1)B+IB=O` or `KAB-2I+B=O` or `KAB^(2)-2B+B^(2)=O` or `KI-2B+B^(2)=O` or `K[(1,0),(0,1)]-2[(2,-1),(2,0)]+[(2,-1),(2,0)][(2,-1),(2,0)] =[(0,0),(0,0)]` or `[(K,0),(0,K)]-[(4,-2),(4,0)]+[(2,-2),(4,-1)]=[(0,0),(0,0)]` or `[(K-2,0),(0,K-2)]=[(0,0),(0,0)]` ot `K=2` (ii) `A^(-1)XA=B` or `A A^(-1)XA=AB` or `IXA=AB` or `XAB=AB^(2)` or `XAB=I` or `XAB^(2)=B` or `XI=B` or `X=B`

Discussion

No Comment Found

Related InterviewSolutions

Let `A=" diag "[3,-5,7]" and "B=" diag "[-1,2,4].` ltbr. Find (i) (A+B) (ii) (A-B) (iii) -5A (iv) (2A+3B).`
A2=A THEN FIND VALUE OF (I+A)2 -3A
If `A=[(1,2),(2,1)]` and `f(x)=(1+x)/(1-x)`, then f(A) isA. `[(1,1),(1,1)]`B. `[(2,2),(2,2)]`C. `[(-1,-1),(-1,-1)]`D. none of these
Id `[1//25 0x1//25]=[5 0-a5]^(-2)`, then the value of `x`is`a//125`b. `2a//125`c. `2a//25`d. none of theseA. `a//125`B. `2a//125`C. `2a//25`D. none of these
If `A=[(a+ib,c+id),(-c+id,a-ib)]` and `a^(2)+b^(2)+c^(2)+d^(2)=1`, then `A^(-1)` is equal toA. `[(a-ib,-c-id),(c-id,a+ib)]`B. `[(a+ib,-c+id),(-c+id,a-ib)]`C. `[(a-ib,-c-id),(-c-id,a+ib)]`D. none of these
If the matrix A is such that `({:(1,3),(0,1):})A=({:(1,1),(0,-1):})`, then what is A equal to ?A. `{:[(1,4),(-1,0)]:}`B. `{:[(1,-4),(1,0)]:}`C. `{:[(1,-4),(0,-1)]:}`D. none of these
If `A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta, sin 2beta] , [sin 2 beta, -cos2beta]]` where `0 lt beta lt pi/2` then prove that `BAB=A^(-1)` Also find the least positive value of `alpha` for which `BA^4B= A^(-1)`A.B.C.D.
If `A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta, sin 2beta] , [sin 2 beta, -cos2beta]]` where `0 lt beta lt pi/2` then prove that `BAB=A^(-1)` Also find the least positive value of `alpha` for which `BA^4B= A^(-1)`
If `A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))]`, then `A(alpha, beta)^(-1)` is equal toA. `A(-alpha, -beta)`B. `A(-alpha, beta)`C. `A(alpha, -beta)`D. `A(alpha, beta)`
`{:A=[(cos^2 alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)]:}` `{:B=[(cos^2 beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)]:}` are two matrices such that the product AB is the null matrix, then `(alpha-beta)` is

Matrices a and B satisfy `AB=B^(-1)`, where `B=[(2,-1),(2,0)]`. Find (i) without finding `B^(-1)`, the value of K for which `KA-2B^(-1)+I=O`. (ii) without finding `A^(-1)`, the matrix X satifying `A^(-1) XA=B`.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment