(adsbygoogle = window.adsbygoogle || []).push({}); Use cross product formula in R^4 to obtain a vector that is orthogonal to rows of A

Please help with first part and check if i answered the questions correctly.

The matrix A =

1 4 -1 2

0 1 0 -1

2 9 -2 2

1. Use cross product formula in R^4 to obtain a vector that is orthogonal to the rows of A.

I multiply the matrix A by a 4x1 matrix X and equate to 0.

Matrix X =

x1

x2

x3

x4

Then i get:

x1+ 4x2 - 3x3 + 2x4 =0

x2 + x4 = 0

2x1 + 9x2 - 2x3 + 2x4 =0

x1 = -4x2 + 3x3 - 2x4

x2 = - x4

x3 = x3

2x4 = -2x1- 9x2 + 2x3

And then... i'm stuck.

2. How is this vector related to the null space of A?

My answer: That vector is perpendicular to the null space of A.

Is this correct and is there another way to put it?

**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!

# Use cross product formula in R^4 to obtain orthogonal vector

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