1.(a) If A is invertible and AB = AC, prove that B = C.
(b) Let A =24
1 1
1 135 explain why A is not invertible.
(c) Let A =24
1 1
1 135, ¯nd 2 matrices B and C, B 6= C such that AB = AC.

2.
(a) If a square matrix A has the property that row 1 + row 2 = row 3, clearly explain why
the matrix A is not invertible.
(b) If any square matrix B has the property that one row equals the sum of multiples of
the other rows, clearly explain why the matrix B is not invertible.
In class, we will show (Section 3.5) that AB is an invertible matrix if and only if A

See attached file for full problem description. #1 and 2 only.

The final answers are:
A is not invertible. Why? For step by ...

Solution Summary

Solutions to the posted problems are given with step by step explanation in such a way that the students understand the procedure and method involved in solving such type of problems and also could use these solutions as model solutions to solve other similar problems using these solutions.

1. Consider the matrices
A = 3 4 1 B = 8 1 5 C = 3 4 1
2 -7 -1 2 -7 -1 2 -7 -1
8 1 5 3 4 1 2 -7 3
Is it possible to find an elementary matrix E such th

One of the problems of storing data in a matrix (a two-dimensional Cartesian structure) is that if not all of the elements are used, there might be quite a waste of space. In order to handle this, we can use a construct called a "sparse matrix", where only the active elements appear. Each such element is accompanied by its two i

Using MatLab, compute H^-1H for various n between 5 and 15. Describe the results and comment on the difference between the MatLab output and what is expected the answer to be (given that H is invertible for all n). At what point does Matlab give a warning indicating that it may not be giving the correct answer?
Try using the

I need help with this problem. I've been working on it for a while and unable to solve it. I need to understand how to solve this problem through examples. With step by step breakdown to fully complete the problem.
Thank you for your help it is greatly appreciated!
(a) Prove that if A and B are both invertible n x n m

Practice problems on determinants and matrices. All questions can be found in the attached file.
Write the matrix equation as a system of equations and solve the system.
■(1&2&3@1&1&1@-1&1&2) {█(x@y@z)┤ = {█(1@12@2)┤
Find the determinant of the given matrix.
■(1&0&6 -1@-6&0&2 4@3&0&6 -2 )

1.
Given the matrices
[010] [100] [100]
A=[101] B= 010] C=[000]
[010] [001] [00-1]
Show that A and B commute, B and C commute but A and C do not.
2.
Show that the matrix
[1 4 0]
[2 5 0]
[3 6 0]
Is not invertible
3.
Find the inv

Please prove the statements shown below:
1. If the elementary matrix E results from performing a certain row operation on an identity matrix Im and if A is an m x n matrix, then the product EA is the matrix that results when this same roe operation is performed on A.
2. Every elementary matrix is invertible, and the invers