# Solve for X. [[-7,-2],[-3,-3]]X + [[-6,-6],[2,-5]] = [[-7,8],[-2,5]]X X=??

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to consider the matrix X, such that:

`X = ((a,b),(c,d))`

Performing the matrix multiplication yields:

`((-7,-2),(-3,-3))*((a,b),(c,d))` = `((-7a - 2c, -7b - 2d),(-3a - 3c, -3b - 3d))`

`((-7,8),(-2,5))*((a,b),(c,d)) = ` `((-7a + 8c, -7b + 8d),(-2a + 5c, -2b + 5d))`

Solving the matrix equation yields:

`((-7a - 2c - 6, -7b - 2d - 6),(-3a - 3c + 2, -3b - 3d - 5)) = ((-7a + 8c, -7b + 8d),(-2a + 5c, -2b + 5d))`

Equating the corresponding members yields:

`{(-7a - 2c - 6 = -7a + 8c),(-7b - 2d - 6 = -7b + 8d),(-3a - 3c + 2 = -2a + 5c),(-3b - 3d - 5 = -2b + 5d):}`

`{(-10c = 6 => c = -3/5),(d = -3/5),(-a = -24/5 - 2 => a = 34/5),(b = 24/5 + 5 => b = -1/5):}`

Hence, evaluating the matrix X, under the given conditions, yields `X = ((34/5,-1/5),(-3/5,-3/5)).`

rakesh05 | High School Teacher | (Level 1) Assistant Educator

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The above system can be written as `[[-7,-2],[-3,-3]]X+[[-6,-6],[2,-5]]=[[-7,8],[-2,5]]X`

orĀ ,

`[[-7,8],[-2,5]]X-[[-7,-2],[-3,-3]]X=[[-6,-6],[2,-5]]`

or,

`[[0,10],[1,8]]X=[[-6,-6],[2,-5]]`

or,

`X=[[0,10],[1,8]]^-1[[-6,-6],[2,-5]]`

or,

`X=[[-4/5,1],[1/10,0]][[-6,-6],[2,-5]]`

or,

`X=[[34/5,-1/5],[-3/5,-3/5]]` .