Solve for Ex and Ey using these two formulas: 1.2-Ex(0.6)+2Ey = 0 and 2Ey-Ex(0.6) = 1.2...

Solve for Ex and Ey using these two formulas: 1.2-Ex(0.6)+2Ey = 0 and 2Ey-Ex(0.6) = 1.2

Please show all the steps.

NOTE: The correct answer for Ex should be 4.25 and Ey should be 1.875. I want to see how they derive the two values.

Solutions

Expert Solution

The given linear equations are 1.2-E_x (0.6)+2E_y = 0 or, 0.6E_x -2E_y = -1.2…(1) and 2E_y-E_x(0.6) = 1.2 or, 0.6E_x -2E_y = -1.2..(2)

Thus, the 2^nd equation is same as the 1^st equation so that we have only 1 equation in 2 unknowns. Therefore, there will be infinite solutions which can be determined as under:

0.6E_x -2E_y = -1.2 or, E_x = -(1.2/0.6) +(2/0.6)E_y = -2+(2/0.6)E_y. Therefore, (E_x , E_y) = (-2+(2/0.6)E_y ,E_y) = (-2,0) + (1/0.6)E_y ( 2, 0.6) = (-2,0) +t( 2, 0.6), where t = + (1/0.6)E_y is an arbitrary real number.

Thus, every solution to the given equation(s ) is a linear combination of the vectors (-2,0) and ( 2, 0.6).

milcah answered 1 year ago

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