# Let vector x = <x_1, x_2> , vector y = <y_1, y_2, y_3> and vector z = <z_1, z_2>. Say that the systems x_1 = 2y_1 + 3y_2 - 5y_3 x_2 = -3y_1 - 4y_2 + 2y_3 and y_1 = 2z_1 - 3z_2 y_2...

Let vector x = <x_1, x_2> , vector y = <y_1, y_2, y_3> and vector z = <z_1, z_2>.

Say that the systems

x_1 = 2y_1 + 3y_2 - 5y_3

x_2 = -3y_1 - 4y_2 + 2y_3

and

y_1 = 2z_1 - 3z_2

y_2 = 3z_1 - z_2

y_3 = z_1 + z_2

Use the matrix product to write vector x in terms of vector z.

### 3 Answers | Add Yours

`[[x_1],[x_2]]=[[2,3,-5],[-3,-4,2]][[y_1],[y_2],[y_3]]` (i)

`[[y_1],[y_2],[y_3]]=[[2,-3],[3,-1],[1,1]][[z_1],[z_2]]` (ii)

from (i) and (ii) ,we have

`[[x_1],[x_2]]=[[2,3,-5],[-3,-4,2]][[2,-3],[3,-1],[1,1]][[z_1],[z_2]] `

`[[x_1],[x_2]]=[[4+9-5,-6-3-5],[-6-12+2,9+4+2]][[z_1],[z_2]]`

`[[x_1],[x_2]]=[[8,-14],[-16,15]][[z_1],[z_2]]`

`x_1=8z_1-14z_2`

`x_2=-16z_1+15z_2`

Ans.

`[[x_1],[x_2]]=[[2,3,-5],[-3,-4,2]][[y_1],[y_2],[y_3]]` (i)

`[[y_1],[y_2],[y_3]]=[[2,-3],[3,-1],[1,1]][[z_1],[z_2]]` (ii)

From (i) and (ii) ,we have

`[[x_1],[x_2]]=[[2,3,-5],[-3,-4,2]][[2,-3],[3,-1],[1,1]][[z_1],[z_2]] `

`[[x_1],[x_2]]=[[2.2+3.3-5.1,-2.3-1.3-1.5],[-3.2-4.3+2.1,3.3+1.4+1.2]][[z_1],[z_2]]`

`[[x_1],[x_2]]=[[8,-14],[-16,15]][[z_1],[z_2]]`

`[[x_1],[x_2]]=[[8z_1-14z_2],[-16z_1+15z_2]]`

`x_1=8z_1-14z_2`

`x_2=-16z_1+15z_2`

Ans.

`[[x_1],[x_2]]=[[2,3,-5],[-3,-4,2]][[y_1],[y_2],[y_3]]` (i)

`[[y_1],[y_2],[y_3]]=[[2,-3],[3,-1],[1,1]][[z_1],[z_2]]` (ii)

From (i) and (ii) ,we have

`[[x_1],[x_2]]=[[2,3,-5],[-3,-4,2]] [[2,-3],[3,-1],[1,1]][[z_1],[z_2]]`

`[[x_1],[x_2]]=[[4+9-5,-6-3-5],[-6-14+2,9+4+2]][[z_1],[z_2]]`

`[[x_1],[x_2]]=[[8,-14],[-18,15]][[z_1],[z_2]] `

which is required solution.