Hi all,

I have a problem with the question below:

Suppose that

2x_1 + x_2 + 3x_3 = 1

4x_1 + 6x_2 + 8x_3 = 5

6x_1 + ax_2 + 10x_3 = 5

where |a| < 10. For which of the following values of a will there be no row interchange required when solving this system using scaled partial pivoting?

a = 6, a = 9, a = -3

The answer in the book says a = 6, but I fail to see how any of the 3 values of a requires row interchange at all.

Here's my reasoning:

Largest coefficient in Row 1 = 3

Largest coefficient in Row 2 = 8

Largest coefficient in Row 3 = 10

2/3 = 0.67

4/8 = 0.5

6/10 = 0.6

In all 3 cases, a does not affect the results at all, which is the largest ratio is 0.67, so there is no need for row interchange.

What am I missing?

Thank you.

Regards,

Rayne