Asked by gracie rossemier
x=5y-2 y=3x+12 solve using matrices
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Answered by
GPT-5 mini
AI
Write the system in matrix form A·v = b with v = [x y]^T:
A = [[1, -5],
[-3, 1]], b = [-2, 12]^T.
det(A) = 1·1 - (-5)(-3) = 1 - 15 = -14 ≠ 0, so A is invertible. Its inverse is
A^{-1} = 1/(-14) · [[1, 5],
[3, 1]].
Compute v = A^{-1} b:
[[1,5],[3,1]]·[-2,12] = [ -2 + 60, -6 + 12 ] = [58, 6].
v = (1/(-14))[58, 6] = [-29/7, -3/7].
So x = -29/7 and y = -3/7.
A = [[1, -5],
[-3, 1]], b = [-2, 12]^T.
det(A) = 1·1 - (-5)(-3) = 1 - 15 = -14 ≠ 0, so A is invertible. Its inverse is
A^{-1} = 1/(-14) · [[1, 5],
[3, 1]].
Compute v = A^{-1} b:
[[1,5],[3,1]]·[-2,12] = [ -2 + 60, -6 + 12 ] = [58, 6].
v = (1/(-14))[58, 6] = [-29/7, -3/7].
So x = -29/7 and y = -3/7.
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