MAT-0060: Elementary Matrices - Ximera

Home » What Is An Elementary Matrix » MAT-0060: Elementary Matrices - Ximera

Maybe your like

Consider the matrices The two matrices have something in common. Can you figure out what it is? (The answer will be given later in the problem.)

Let’s compute and .

Observe that multiplying by on the left results in multiplying the second row of by , while multiplying by on the left results in multiplying the third row of by .

Now we need to return to the question of what and have in common. Both matrices were obtained from the identity matrix by multiplying one row of the identity by a non-zero constant. Matrices and were obtained from by multiplying one row of by and respectively. Multiplying by (or ) on the left affects in the same way.

Matrix does not have to be a square matrix. Try finding and for

Observe that and have the same effect on as they did on .

Tag » What Is An Elementary Matrix