Chemical Engineering Hand Written_Notes_Part_28

# Chemical Engineering Hand Written_Notes_Part_28 - 58 3...

This preview shows pages 1–2. Sign up to view the full content.

58 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES or equivalently the n column vectors are not linearly independent. Thus, both these geometric interpretations are consistent with each other. Now, to understand behavior of solutions of type (1.5), we can de fi ne four fundamental spaces associated with matrix A Definition 22 . ( Column Space): The space spanned by column vectors of matrix A is de fi ned as column space of the matrix and denoted as R ( A ) . Definition 23 . ( Row Space): The space spanned by row vectors of matrix A is called as row space of matrix A and denoted as R ( A T ) . Definition 24 . ( Null space): The set of all vectors x such that A x = ¯ 0 is called as null space of matrix A and denoted as N ( A ) . A non-zero null space is obtained only when columns of A are linearly de- pendent. If columns of A are linearly independent, then N ( A ) { ¯ 0 } . Definition 25 . ( Left Null Space) : The set of all vectors y such that A T y = ¯ 0 is called as null space of matrix A and denoted as N ( A T ) .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern