A-2-7-3-9-4-A-a-b-c-d-Find-the-all-of-different-matrices-A-i-If-a-b-c-d-Z-ii-If-a-b-c-d-R-

Question Number 93534 by naka3546 last updated on 13/May/20

A^{2} = (\begin{matrix} 7 & 3 \\ 9 & 4 \end{matrix}) \Rightarrow A = (\begin{matrix} a & b \\ c & d \end{matrix})

F i n d t h e a l l o f d i f f e r e n t m a t r i c e s A

(i) . I f a, b, c, d \in Z

(i i) . I f a, b, c, d \in R^{+}

Answered by prakash jain last updated on 13/May/20

A^{2} = [\begin{matrix} a^{2} + b c & a d + b d \\ a c + c d & b c + d^{2} \end{matrix}]

a^{2} + b c = 7

a d + b d = 3

a c + c d = 9

b c + d^{2} = 4

Z^{+}

a^{2} - d^{2} = 3 \Rightarrow a + d = 3, a - d = 1

a = 2, d = 1

b = 1

c = 3

A = [\begin{matrix} 2 & 1 \\ 3 & 1 \end{matrix}]

Commented by naka3546 last updated on 13/May/20

Commented by naka3546 last updated on 13/May/20

I h a v e t o f i n d t h e d i f f e r e n t t w o m a t r i c e s m o r e .

Commented by prakash jain last updated on 13/May/20

One more solution exists for Real numbers case. i am still trying to solve real number cae

Commented by prakash jain last updated on 13/May/20

in z there are two soltion, one that i gave for z+. another one with sign changed for all numbers