Answer :
To write the system of linear equations in the form Ax = b, we rearrange the given equations:
1) X₁ - 5X₂ + 2XY = 15
2) -3X₁ + X₂ + X₃ = -2
3) -2X₂ + 5XY = 19
Now we can write this system of equations in matrix form:
⎡ 1 -5 2⋅Y ⎤ ⎡ X₁ ⎤ ⎡ 15 ⎤
⎢ -3 1 1 ⎥ ⋅ ⎢ X₂ ⎥ = ⎢ -2 ⎥
⎣ 0 -2 5⋅Y ⎦ ⎣ X₃ ⎦ ⎣ 19 ⎦
This gives us the equation Ax = b, where:
A = ⎡ 1 -5 2⋅Y ⎤
⎢ -3 1 1 ⎥
⎣ 0 -2 5⋅Y ⎦
x = ⎡ X₁ ⎤
⎢ X₂ ⎥
⎣ X₃ ⎦
b = ⎡ 15 ⎤
⎢ -2 ⎥
⎣ 19 ⎦
To solve this matrix equation for x, we can use matrix algebra. Assuming Y is a constant, we can find the inverse of matrix A, multiply it by vector b to solve for x:
x = A^(-1) * b
Learn more about matrix algebra here:
https://brainly.com/question/29428869?
#SPJ11
