- #1

DryRun

Gold Member

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**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?

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