Could s.o help me this problem. We are doing the second semester of the first year of ho chi minh city uni of tech. (HCMUT) . This is linear algebra course

Question

Doing the row operation -6R2 + R3-> R3 on a matrix A(4*4) this is equivalent to multiplying A by the matrix D. Find D and figure out it is on the left or right of the A

Answer 1

The way to find D in this case is to apply the row operations to the 4x4 identity matrix I. This matrix is

[ 1 0 0 0 ]

[ 0 1 0 0 ]

[ 0 0 1 0 ]

[ 0 0 0 1 ]

Hence, after applying -6R2 + R3 --> R3, we get the matrix

[ 1 0 0 0 ]

[ 0 1 0 0 ]

[ 0 -6 1 0 ]

[ 0 0 0 1 ]

To check whether this matrix D acts by multiplying on the right or the left, let's take some sample matrix, maybe the matrix (I really just chose this randomly) C =

[ 1 1 0 0 ]

[ 0 1 1 0 ]

[ 1 0 0 1 ]

[ 0 1 0 1 ]

Multiplying D * C gets the correct result, whereas multiplying C * D gets some other matrix. Hope this helps!