Math, asked by sreesagar2468, 1 year ago

If A=[1 −2
2 −1], B=[a 1
b −1] and (A + B)2 = A2 + B2, Find a and b. ​

Answers

Answered by amitnrw
19

Answer:

a =1 & b = 2

Step-by-step explanation:

A =  1    - 2

     2      -1

A² =     1*1  + (-2*2)       1*(-2) + (-2)(-1)    

          2*1  + (-1)2          2*(-2) + (-1)(-1)

A² =   -3     0

         0      -3

B =    a         1

        b        -1

B² =   a²+b        a-1

        ba - b       b+1

A² + B²  =     a² + b - 3           a-1

                    ba - b                 b-2

A+B  =    a +1      -1

             a +b       -2

(A+B)² =  a² + 2a - b - 1              1 -a

               ab + 2a - b - 2            2-b

(A+B)² = A² + B²

Equating each term

a² + b - 3 = a² + 2a - b - 1 => b = a + 1

a-1 = 1-a  => 2a = 2 => a = 1

ba - b = ab + 2a - b - 2 => 2a = 2 => a = 1

b-2 = 2- b => 2b = 4 => b = 2

b = a + 1 is satisfied by a = 1 & b =2

Answered by Robonaut
7

(A+B)2 =

| (a+1)2-b+2 2-a-1 |

| (b+2)(a+1)-2b-4 4-b-2 |

A2 + B2 =

| a2+b-3 a-1 |

| ab-b. b-2 |

If (A+B)2 = A2 + B2 then 2a - a = a - 1 and b-2 = 4 - b - 2

Hence a = 1 & b = 2

Similar questions