Page 459 - Excel for Scientists and Engineers: Numerical Methods

436 EXCEL: NUMERICAL METHODS

1 1. I used Goal Seek.. . with the cell containing the formula MDETERM as the
target cell and the cell containing the (1 , 1) element of the matrix as the
changing cell. The cell value 0.25 gives a determinant value of zero. Two
elements of the matrix cannot be varied so as to give a zero value: the (1 , 3)
element and the (3, 1) element.

Chapter 9 Simultaneous Equations

1. Using the GaussElim function, x1 = 40.6752697, x2 = -77.86744959,
~3 = 3.1 11657335, ~4 = 10.63794438.

2. Using the GaussElim function, 11 = 1 , 12 = 0,13 = 1.

3. Using the GaussElim function, x1 = 0.621563612,~2 =-5.5~10-~~,
~3 = 0.216058954, ~4 =0.758779009.

4. [Co2'] = 0.0533, mi2+] = 0.1 125, [Cu2'] = 0.1022 mo1L

5. (a) Not solvable. Row 3 is a multiple of row 1.

6. Using the GaussElim function, XI = 29.746, x2 = 19.991, x3 = -20.487,
x4 = 4.455, x5 = 48.369, xfj = -8.270.

7. Using the SimultEqNL custom function, x = 0.707,~ = 0.707.

8, Using the SimultEqNL custom function, x = -1 , y = 2, z = -1

Chapter 10 ODES with Initial Conditions

1. I used the Rungel custom function. Set up the spreadsheet with three
columns: x, y, y'.

2. I used the Rungel custom function. Set up the spreadsheet with three
columns: x, y, yl. The exact expression for y is given in the answer
spreadsheet.