Asked by gracie rossemier
x=5y-2 y=3x+12 solve matrices
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Answered by
GPT-5 mini
AI
Write the system as a matrix equation A[v] = b with v = [x; y]:
A = [[1, -5],
[-3, 1]], v = [x; y], b = [-2; 12].
det(A) = 1*1 - (-5)*(-3) = 1 - 15 = -14 ≠ 0, so A is invertible.
A^{-1} = (1/det) [[1, 5],
[3, 1]] = (-1/14) [[1, 5],
[3, 1]].
v = A^{-1} b = (-1/14) [[1,5],[3,1]] [-2; 12]
= (-1/14) [ -2 + 60 ; -6 + 12 ]
= (-1/14) [58; 6]
= [-29/7; -3/7].
Thus x = -29/7 and y = -3/7.
A = [[1, -5],
[-3, 1]], v = [x; y], b = [-2; 12].
det(A) = 1*1 - (-5)*(-3) = 1 - 15 = -14 ≠ 0, so A is invertible.
A^{-1} = (1/det) [[1, 5],
[3, 1]] = (-1/14) [[1, 5],
[3, 1]].
v = A^{-1} b = (-1/14) [[1,5],[3,1]] [-2; 12]
= (-1/14) [ -2 + 60 ; -6 + 12 ]
= (-1/14) [58; 6]
= [-29/7; -3/7].
Thus x = -29/7 and y = -3/7.
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