Elementary Operations of Type Two Consider the row operation that replaces row s with row s plus a non-zero scalar, λ, times row t. Define E to be the matrix so that E kk
​
=1 for all k,E st
​
=λ, and E ij
​
=0 for all other entries i,j. It is easy to verify that left multiplication by E achieves the given row operation. Exercise 42. What is the elementary matrix that replaces row 2 of a 5×n matrix with row 2 plus 1.3 times row 4 ? Exercise 43. Show that E is invertible by finding the inverse of E. Note that E −1
is also an elementary matrix of the second type.