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Given matrix A ,show A^2=10A ? A=(3   2   1 )      (6   4   2)      (9  ...

yapayapa | Honors

Posted August 4, 2013 at 3:32 PM via web

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Given matrix A ,show A^2=10A ?

A=(3   2   1 )

(6   4   2)

(9   6   3)

Tagged with math, matrix, power

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 4, 2013 at 4:16 PM (Answer #1)

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You need to evaluate the square of matrix A, such that:

`A^2 = A*A`

`A^2 =` `((3,2,1),(6,4,2),(9,6,3))*((3,2,1),(6,4,2),(9,6,3))`

Performing the matrices multiplication, yields:

`A^2 = ((9+12+9,6+8+6,3+4+3),(18+24+18,12+16+12,6+8+6),(27+36+27,18+24+18,9+12+9))`

`A^2 = ((30,20,10),(60,40,20),(90,60,30))`

`A^2 = ((3*10,2*10,1*10),(6*10,4*10,2*10),(9*10,6*10,3*10))`

Factoring out 10 yields:

`A^2 = 10*((3,2,1),(6,4,2),(9,6,3))`

Since `A = ((3,2,1),(6,4,2),(9,6,3))` , yields:

`A^2 = 10*A`

Hence, testing the validity of the statement `A^2 = 10A` , under the given conditions, yields that `A^2 = 10*A` holds.