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Consider the matrix

A = 1 3 -5
0 -2 5
3 -1 6
Suppose B is the reduced row- echelon form (RREF) of A. Find a
matrix U such that B = UA.

User Dan Schnau
by
8.3k points

1 Answer

4 votes

Answer:

To find the matrix U such that B = UA we can start by performing row operations on matrix A to reduce it to its row-echelon form (RREF which will give us matrix B.

Given matrix A:

A = 1 3 -5

0 -2 5

3 -1 6

We can perform row operations on A to reduce it to RREF:

1. Multiply row 2 by 3 and add it to row 1:

A' = 1 3 -5

0 -2 5

0 8 -4

2. Multiply row 3 by -1/2 and add it to row 2:

A' = 1 3 -5

0 -2 5

0 0 3

3. Multiply row 3 by 1/3:

A' = 1 3 -5

0 -2 5

0 0 1

This is the row-echelon form B. Now we can find the matrix U such that B = UA.

Let U be the matrix of row operations performed on A to obtain B:

U = 1 0 0

0 1 0

-3 1 1/3

To verify that B = UA let's multiply U by A:

UA = 1 0 0 * 1 3 -5 = 1 3 -5

0 1 0 0 -2 5 0 -2 5

-3 1 1/3 3 -1 6 0 0 1

As we can see B = UA.

User Arpan Solanki
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8.2k points