🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →

HomeClass Notes1,200,000CA670,000

MATH125 Lecture Notes - Lecture 6: Row And Column Vectors, Coefficient Matrix, Augmented Matrix

22 views3 pages

amaranthoyster518

28 Apr 2016

School

University of Alberta

Department

Course

Professor

Vladimir Chernousov

For unlimited access to Class Notes, a Class+ subscription is required.

peachmoose0 and 4 others unlocked

MATH125 Full Course Notes

MATH125 Full Course Notes

Document Summary

Definition: let a and b be matrices with sizes a=mxn and b=nxr then the product of a*b is the matrix c of size mxr given by c=cij where cij=ai1*b1j+ai2*b2j++ainbnj. Therefore this is the dot product of the ith row of a with the jth column of b. The columns of matrix a must equal the rows of matrix b. See in class notes for example: it is too large to put in here. This shows that a*x=b, and as an augmented matrix we would write [a|b] A has mxn x has nx1 has mx1. Observation: in the system we have the following column notation. This system has a solution if and only if the column b is a linear combination of the columns a1, a2,,an. The set of all linear combinations was denoted by spane(a1, a2,,a) therefore b is within the span of the system.

Related textbook solutions

Calculus

ISBN: 9781319050733

Single Variable Calculus: Early Transcendentals

4th Edition, 2018

ISBN: 9781337687805

CALCULUS:EARLY TRANSCENDENTALS

ISBN: 9781319050740

Related Documents

MATH125 Lecture Notes - Lecture 27: Laplace Expansion, Main Diagonal, Triangular Matrix

carminelocust146

MATH125 Lecture Notes - Lecture 4: Row Echelon Form, Augmented Matrix, Coefficient Matrix

amaranthoyster518

MATH125 Study Guide - Final Guide: A143 Road, Adjoint, Laplace Expansion

cerisegiraffe538

Related Questions

1. Consider the augmented matrix: (linear algebra)

a) Convert the matrix to echelon form

b) Obtain the reduced echelon form from the previous step

c) write a solution set for the corresponding system of equations

Please help with all questions. Will rate ASAP.

This question addresses inverse transformations from a conceptual standpoint, a. Suppose that a linear transformation T: x rightarrow Ax from A to A takes some nonzero vector x to 0. Can this transformation be reversed? Does A exist? Suppose that a linear transformation T: x rightarrow Ax from is not one-to-one. What does that tell you about the set of vectors b that can be produced by applying the transformation T to all vectors x in A? How do you know, in that case, that the transformation T is not reversible (i.e. that there does not exist an inverse transformation with the standard matrix A-1 that can be applied to the result of Ax to restore the vector x to its original value)? Suppose that a linear transformation T: x rightarrow Ax from A to A is not onto. What does that tell you about the set of vectors b that can be produced by applying the transformation T to all vectors x in A? Is it possible for a linear transformation x rightarrow Ax from A to A to be one-to-one but not onto, or onto but not one-to-one? If so, please give examples of each case. If not, explain why not. Is it possible for an arbitrary linear transformation x rightarrow Ax from A to B to be one-to-one but not onto, or onto but not one-to-one? If so. please give examples of each case. If not, explain why not. For what values of {a. b. c, d. e.f. a. h. i.j } will the matrix A = invertible? what is the least amount of partitioning that needs to be applied to M; to make M1 and M2 conformable for block multiplication? What is the product M = M1, M2 that you obtain using block multiplication with these partitions? What is the product M = M1 M2. that you obtain by multiplying the two matrices without partitioning? For which three values of a is the matrix B = not invertible, and why If M1 and M2 arc partitioned matrices such that M1 For each matrix product shown below, draw in the partitions that would need to be added to make the multiplication possible: Describe in general how the sizes of each of the partitions(#rows, #columns) in a matrix product C = AB are defined by the sizes of the partitions in each of the matrices A and B when partitioned matrices are multiplied.

This is Linear Algebra, please help!