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puskmobi
@puskmobi
December 2021
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Используя матричные операции, выразить x1, x2, x3 через z1, z2, z3
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Эль96
Y1 = -3X2-2X3 Z1 = -7Y1-2Y2+5Y3
Y2 = X1-2X2-X3 Z2 = -Y1+Y3
Y3 = X1-5X2-4X3 Z3 = Y2
Z3 = Y2 = X1-2X2-X3
Z2 = -Y1+Y3 = 3X2+2X3+X1-5X2-4X3 = X1-2X2-2X3
Z1 = -7Y1-2Y2+5Y3 = 21X2+14X3-2X1+4X2+2X3+5X1-25X2-20X3 = 3X1-4X3
Z1 = 3X1-4X3
Z2 = X1-2X2-2X3
Z3 = X1-2X2-X3
1) Z2-Z3 = X1-2X2-2X3-X1+2X2+X3
Z2-Z3 = -X3
X3 = Z3-Z2
2) Z1 = 3X1-4X3
Z1 = 3X1-4Z3+4Z2
3X1 = Z1+4Z3-4Z2
3X1 = Z1+4Z3-4Z2
X1 = 1/3Z1+4/3Z3-4/3Z2
3) Z3 = X1-2X2-X3
2X2 = 1/3Z1+4/3Z3-4/3Z2-Z3+Z2-Z3
2X2 = 1/3Z1+4/3Z3-4/3Z2-Z3+Z2-Z3
2X2 = 1/3Z1-1/3Z2-2/3Z3
X2 = 1/6Z1-1/6Z2-1/3Z3
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Answers & Comments
Y2 = X1-2X2-X3 Z2 = -Y1+Y3
Y3 = X1-5X2-4X3 Z3 = Y2
Z3 = Y2 = X1-2X2-X3
Z2 = -Y1+Y3 = 3X2+2X3+X1-5X2-4X3 = X1-2X2-2X3
Z1 = -7Y1-2Y2+5Y3 = 21X2+14X3-2X1+4X2+2X3+5X1-25X2-20X3 = 3X1-4X3
Z1 = 3X1-4X3
Z2 = X1-2X2-2X3
Z3 = X1-2X2-X3
1) Z2-Z3 = X1-2X2-2X3-X1+2X2+X3
Z2-Z3 = -X3
X3 = Z3-Z2
2) Z1 = 3X1-4X3
Z1 = 3X1-4Z3+4Z2
3X1 = Z1+4Z3-4Z2
3X1 = Z1+4Z3-4Z2
X1 = 1/3Z1+4/3Z3-4/3Z2
3) Z3 = X1-2X2-X3
2X2 = 1/3Z1+4/3Z3-4/3Z2-Z3+Z2-Z3
2X2 = 1/3Z1+4/3Z3-4/3Z2-Z3+Z2-Z3
2X2 = 1/3Z1-1/3Z2-2/3Z3
X2 = 1/6Z1-1/6Z2-1/3Z3