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(i)A^2-B^2!=(A+B)(A-B) Explain why in ge...

`(i)A^2-B^2!=(A+B)(A-B)` Explain why in general(0 A? -8^@ = (A + B) (A - B),

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(i)A^(2)-B^(2)!=(A+B)(A-B) Explain why in general( (0A?-8^(^^)@=(A+B)(A-B)

Explain eohy in general(ii) (A+-B)^(2)!=A^(2)+B^(2)+-2AB

Knowledge Check

  • If A = [{:(i, 0),(0,i):}] and B = [{:(0,-i),(-i,0):}] , then (A + B)(A - B) equals

    A
    `A^(2) + B^(2)`
    B
    `A^(2) - B^(2)`
    C
    `A^(2) + 2AB + B^(2)`
    D
    None of these

  • If 3a ^(2) = b ^(2) ne 0, then the value of ((a + b ) ^(2) - (a - b ) ^(3))/((a + b ) ^(2) + (a-b) ^(2)) is:

    A
    `3/2 b`
    B
    b
    C
    `1/2b`
    D
    `2/3 b`

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    If A and B are square matrices of the same order,explain,why in general (A+B)^(2)!=A^(2)+2AB+B^(2)( ii) (A-B)^(2)!=A^(2)-2AB+B^(2)( iii) (A+B)(A-B)!=A^(2)-B^(2)

    If A = 125 and B=8, then what is the value of (A+B)^3- (A-B)^3- 6B(A^2-B^2) ? यदि A = 125 तथा 8B= है, तो (A+B)^3- (A-B)^3- 6B(A^2-B^2) का मान क्या है?

    (a) Factorize a^(2) - (b -8) a - 8b

    Let A,B and I (identity matrix) be the matrices of order 4 such that A=[a_(I)]_(4xx4) ' where a_(lj){{:(0 if i = j),(1 if i ne j):}and A =B -I {:(,"Column-I",,"Column-II"),((A),|B|=,,(P)4),((B),|B^(2)-4B+I|= ,,(Q)0),((C),-4+|B^(3)+B^(2)-8B|=,,(R)-1),((D),-1+|A^(-1)+I|"is greater than",,(S)-4),(,,,(T)1):}

    If A and B are square matices of the same order such that A^2=A,B^2=B,AB=BA=0 then (A) AB^2=0 (B) (A+B)^2=A+B (C) (A-B)^2=A+B (D) none of these

    Prove that [(a^(2) + b^(2))/(a + b)]^(a + b) gt a^(a) b^(b) gt {(a + b)/(2)}^(a + b) , where a,b gt 0

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