Question

If A^2 = [ 7 10 ] find A. Help Please.
[ 15 22 ]

Answer 1

[ 7 10 ]
[ 15 22 ] <---- matrix A^2

Answer 2

help please?...

Answer 3

Trace =7+22=29
det=7*22-10*15=139
let S^2=det
and t^2=Trace+2s
S=+-sqrt (139)=+13,-13
t=+-sqrt (29+13)=+sqrt 42,-sqrt42
t=+-sqrt(29-13)=4,-4

so for A^2=[ a b]
[c d]
A=1/t [a+s b]
[c d+s]

so u wud have more than one matrix

Answer 4

\[A=\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\\\]
find A^2 parametric
then solve the system of equation

Answer 5

i think ull have 16 matrix of A :o

Answer 6

@ikram002p about the det=7*22-10*15=139...
its 154-150 right?... it is equal to 139?..

Answer 7

ohh sry i made a typo , yess
154-150=4 :o
so i need to check every thing nw :(

Answer 8

it's alright...

Answer 9

Trace =7+22=29
det=7*22-10*15=4
let S^2=det
and t^2=Trace+2s
S=+-sqrt (4)=+2,-2
t=+-sqrt (29+2*2)=+sqrt 33,-sqrt33
t=+-sqrt(29-2*2)=+5,-5

Answer 10

let me see one solution
so for A^2=[ a b]
[c d]
A=1/t [a+s b]
[c d+s]
when
t=5
s=2

A=1/5 [7+2 10]
[15 22+2]

A=[9/5 2]
[3 24/5]

lets check from A^2

Answer 11

umm.. isn't
t=5
and s=-2
would be better?
because it will become,
1/5 [ 7-2 10 ]
[ 15 22-2 ]
...
1/5 [ 5 10 ]
[ 15 20 ]
therefore,
[ 1 2 ]
A = [ 3 4 ]
umm, check me if I'm wrong...

Answer 12

ur right but as i said there is 16 matrix of A
that gives u A^2 as u posted :D
so u got one solution of 16

Answer 13

oh. ^^ ok thanks. ummm, I know I'm asking too much but does this procedure also applicable if I would be looking for the root of a 3x3 matrix?

Answer 14

NO , this procedure only work for 2×2 matrix

Answer 15

so... looking for the root of a 3x3 matrix would be more complex?

Answer 16

here u can check quickly from the root
http://ncalculators.com/matrix/2x2-matrix-multiplication-calculator.htm

Answer 17

no its not complecated
give a matrix
A = [x1 x2 x3]
[x4 x5 x6]
[x7 x8 x9]
then find A^2
so u wud have a linear system of equation
hmmm u cud solve it for 9 variable
or use a program that solve linear equations
its easy lol

Answer 18

umm, can you give an example if it's ok with you?

Answer 19

u give me an example ^^
and ill solve it for u

Answer 20

ok... hmm. wait.

Answer 21

[ 2 1 2 ]
A = [ 3 -3 -4 ]
[ 4 -1 2 ]

Answer 22

like this?

Answer 23

oh that must be A^2..

Answer 24

ok u creat this example or u find it in a book ?
cuz if u creat it it might not work
or well have complex number got me ?

Answer 25

oh... I just create it... ^^ ' sorry

Answer 26

huh lol
humm wud u like to work on it ?

Answer 27

[ 1 2 1 ]
A^2 = [ 2 1 1 ]
[ 2 1 2 ] I think smaller elements would be simple (I hope)
how about this?

Answer 28

I just created it..

Answer 29

do u have matlab program ?
cuz if u use matlab there is a code that
gives u the the root in few sec

Answer 30

ok... lets work on it lol

Answer 31

A = [x1 x2 x3]
[x4 x5 x6]
[x7 x8 x9]
find A^2

Answer 32

umm, no. don't know matlab program. sorry..

Answer 33

ok ^^

Answer 34

A^2= [x1 x2 x3] [x1 x2 x3]
[x4 x5 x6] [x4 x5 x6]
[x7 x8 x9] [x7 x8 x9]

Answer 35

can u do the multiple thing ??

Answer 36

yes

Answer 37

ok wat u r waiting for lol
do it :P

Answer 38

[ 30 36 42 ]
A^2 = [ 66 81 96 ]
[ 102 126 150 ]
am I correct? umm, by the way, what's the "x" infront of the numbers?

Answer 39

lol no !
not the matrix u gave
the matrix i gave u

Answer 40

yes yes, that's the 123456789 matrix..

Answer 41

(_ _) sorry if I'm too bad at this...

Answer 42

A^2= [x1 x2 x3] [x1 x2 x3]
[x4 x5 x6] [x4 x5 x6]
[x7 x8 x9] [x7 x8 x9]
=[x1*x1+x2*x4+x3*x7 x1*x2+x2*x5+x3*x8 x1*x3+x2*x6+x3*x9]
[x4*x1+x5*x4+x6*x7 x4*x2+x5*x5+x6*x8 x4*x3+x5*x6+x6*x9]
[x7*x1+x8*x4+x9*x7 x7*x2+x8*x5+x9*x8 x7*x3+x8*x6+x9*x9 ]

ok ?

Answer 43

yes, that's what I did.

Answer 44

lol ok lets continue :P

Answer 45

what's the "x" infront of the numbers?

Answer 46

[x1*x1+x2*x4+x3*x7 x1*x2+x2*x5+x3*x8 x1*x3+x2*x6+x3*x9] [1 2 1 ] [x4*x1+x5*x4+x6*x7 x4*x2+x5*x5+x6*x8 x4*x3+x5*x6+x6*x9]= [2 1 1] [x7*x1+x8*x4+x9*x7 x7*x2+x8*x5+x9*x8 x7*x3+x8*x6+x9*x9 ] [2 1 2]

x1,......,x9 are variables u can put a,b,c..... instead ok ??

Answer 47

ok

Answer 48

x1*x1+x2*x4+x3*x7 =1
x1*x2+x2*x5+x3*x8=2
x1*x3+x2*x6+x3*x9=1
x4*x1+x5*x4+x6*x7=2
x4*x2+x5*x5+x6*x8=1
x4*x3+x5*x6+x6*x9=1
x7*x1+x8*x4+x9*x7=2
x7*x2+x8*x5+x9*x8=1
x7*x3+x8*x6+x9*x9=2
so u have 9 equation solve to find
\(x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9\)

Answer 49

nw solving those equation lol
u need a program
or if u really good solve them
:D

Answer 50

O.O .....

Answer 51

huh :P
in wat class u r ?

Answer 52

what.. class?
mmm, advanced algebra?

Answer 53

ok i guess u dnt need to solve qs like this
anf u had to, theyll give u simple numbers or somthin
u just need to knw how to make equations
not solving them ok ?

Answer 54

ok. ^^

Answer 55

is there an equation for the 2x2 matrix above?

Answer 56

i guess this would be my last question, I'd already took too much of your time...

Answer 57

yess there is just use @amoodarya method

Answer 58

\(A=\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\\\)
\(A^2=\left[\begin{matrix}a×a+b×c & a×b+b×d \\ c×a+d×c & c×b+d×d\end{matrix}\right]\\\)
\(A^2=\left[\begin{matrix}7 & 10 \\ 15 & 22\end{matrix}\right]\\\)
\(\left[\begin{matrix}7 & 10 \\ 15 & 22\end{matrix}\right]=\left[\begin{matrix}a×a+b×c & a×b+b×d \\ c×a+d×c & c×b+d×d\end{matrix}\right]\)
\(a^2+bc=7\)
\(ab+bd=10\)
\(ac+dc=15\)
\(cb+d^2=22\)

Answer 59

ok good luck g2g ^^

Answer 60

ok, thanks. ^^

Answer 61

np