LetA be a `2xx2`matrix with real entries. Let I be the `2xx2`identity matrix. Denote by tr (A), the sumof diagonal entries of A. Assume that `A^2=""I`.Statement1: If `A!=I`and `A!=""-I`, then det `A""=-1`.Statement2: If `A!=I`and `A!=""-I`,then `t r(A)!=0`.(1)Statement 1is false, Statement `( 2) (3)-2( 4)`is true(6)Statement 1is true, Statement `( 7) (8)-2( 9)`(10)is true, Statement `( 11) (12)-2( 13)`is a correct explanation forStatement 1(15)Statement 1is true, Statement `( 16) (17)-2( 18)`(19)is true; Statement `( 20) (21)-2( 22)`is not a correct explanationfor Statement 1.(24)Statement 1is true, Statement `( 25) (26)-2( 27)`is false.A. Statement -1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1B. Statement -1 is true, Statement - 2 is true, Statement -2 is not a correct explanation for Statement-1C. Statement-1 is true, Statement-2 is falseD. Statement-1 is false, Statement-2 is true

LetA be a `2xx2`matrix with real entries. Let I be the `2xx2`identity

1.	LetA be a `2xx2`matrix with real entries. Let I be the `2xx2`identity matrix. Denote by tr (A), the sumof diagonal entries of A. Assume that `A^2=""I`.Statement1: If `A!=I`and `A!=""-I`, then det `A""=-1`.Statement2: If `A!=I`and `A!=""-I`,then `t r(A)!=0`.(1)Statement 1is false, Statement `( 2) (3)-2( 4)`is true(6)Statement 1is true, Statement `( 7) (8)-2( 9)`(10)is true, Statement `( 11) (12)-2( 13)`is a correct explanation forStatement 1(15)Statement 1is true, Statement `( 16) (17)-2( 18)`(19)is true; Statement `( 20) (21)-2( 22)`is not a correct explanationfor Statement 1.(24)Statement 1is true, Statement `( 25) (26)-2( 27)`is false.A. Statement -1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1B. Statement -1 is true, Statement - 2 is true, Statement -2 is not a correct explanation for Statement-1C. Statement-1 is true, Statement-2 is falseD. Statement-1 is false, Statement-2 is true
Answer» Correct Answer - C Let `A = [[1,0],[0,-1]]or [[-1,0],[0,1]]` Then `A^(2) = I` `therefore A = abs((1,0),(0,-1))= - 1 and tr (A)=0`

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

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment