MATH116 Lecture Notes - Lecture 4: Row And Column Spaces

• School: University of Waterloo
• Department: Mathematics
• Course: MATH116
• Professor: Florian Girelli

Document Summary

I will keep going a little more to convert combinations of three-dimensional vectors into linear algebra. If the vectors are v = (1, 2, 3) and w = (1, 3, 4), put them into the columns of a matrix: To nd combinations of those columns, multiply the matrix by a vector (c, d): We call it the column space of the matrix. (for these two columns, that space is a plane. ) To decide if b = (2, 5, 7) is on that plane, we have three components to get right. The vector b = (2, 5, 7) does lie in the plane of v and w. If the 7 changes to any other number, then b won"t lie in the plane it will not be a combination of v and w, and the three equations will have no solution. Now i can describe the rst part of the book, about linear equations ax = b.