Home
Class 11
MATHS
Statement-1:If A=[{:(,a^(2)+x^(2),ab-cx,...

Statement-1:If A=`[{:(,a^(2)+x^(2),ab-cx,ac+bx),(,ab+xc,+b^(2)+x^(2),+bc-ax),(,ac-bx,bc+ax,c^(2)+x^(2))]:} and B=[{:(,x,c,-b),(,-c,x,a),(,b,-a,x):}] "then" |A|=|B|^(2)`

A

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 4

B

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 4

C

Statement 1 is true, Statement 2 is False

D

Statement 1 is False, Statement 2 is true

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, statement 2 true.
i.e., `|adj A| = |A|^(n-1)`
`:. |B| = |A|^(n-1) " " [ :' |B| = |adj A|]`
`rArr Delta_(2) = Delta_(1)^(2)` [ `:' Delta_(2)` is the determinant of the matrix of cofactors]
Hence, both the statement are true and statement 2 is a correct explanation for statement 1
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|92 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|74 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

Show that |{:(a^(2)+x^(2),ab-cx,ac+bx),(ab+cx,b^(2)+x^(2),bc-ax),(ac-bx,bc+ax,c^(2)+x^(2)):}|=|{:(x,c,-b),(-c,x,a),(b,-a,x):}|^(2) .

Statement I If A=[(a^2+x^2,ab-cx,ac+bx),(ab+cx,b^2+x^2,bc-ax),(ac-bx,bc+ax,c^2+x^2)] and B[(x,c,-b),(-c,x,a),(b,-a,x)] , then |A|=|B|^2 Statement II A^c is cofactor of a square matrix A of order n, then |A^c|=|A|^(n-1)

The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,ac,bc,c^(2)(1+x)):}| is divisible by

Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),(ca,,bc,,a^(2)+b^(2)):}|=4a^2b^2c^2

If A=[{:(0,c,-b),(-c,0,a),(b,-a,0):}] and B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , then (A+B)^(2)=

What is |{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}| equal to ?

Prove the following by multiplication of determinants and power cofactor formula |{:(0,c,b),(c,0,a),(b,a,0):}|^(2)=|{:(b^(2)+v^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b^(2)):}| =|{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}|=4a^(2)b^(2)c^(2)

"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that " f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2)) .

"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that " f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2)) .

|[x^2+a^2,ab,ac] , [ab,x^2+b^2,bc] , [ac,bc,x^2+c^2]|=