Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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. Also, I can solve all 3 linear systems without row interchanging at all.

What am I missing?

Thank you.

Regards,

Rayne

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Scaled Partial Pivoting

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**