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^+


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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
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