lecture3compl-09[1] - Math 18.02(Spring 2009 Lecture 3...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 18.02 (Spring 2009): Lecture 3 Matrices. Inverse Matrices February 6 Reading Material: From Course Notes M. Last time: Cross product and determinant Today: Matrices and Inverse Matrices Recall: A matrix A is defined as A = a 11 a 12 · · · a 1 n . . . a m 1 a m 2 a mn = ( a i,j ) n = # columns and m = # rows hence A is a m × n matrix. 2 Matrix Arithmetic Addition: If A, B are m × n matrices then A + B is obtained by adding entries in the same location . Multiplication by scalar: Given a matrix A = ( a ij ) and a scalar c we define the new matrix cA as cA = ( ca ij ) , This means that we have to multiply every entry of A by the scalar c . 1
Image of page 1

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

View Full Document Right Arrow Icon
Mutiplication of two matrices: If A is a m × n and B is a n × s matrix then A · B is a m × s matrix such that its c ij entry is given by ( a i 1 a i 2 · · · a in ) · b 1 j b 2 j . . . b nj = c ij i = 1 , . . . , m j = 1 , . . . , s c ij = row i · col j = n k =1 a ik b kj dot product so A ( m × n ) times B ( n × s ) A · B ( m × s ) . Observe that it is not always possible to multiply two matrices. You need in
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern