3 6 6 Read section 3 4 and then try the following a Find the matrix E which swaps the first and second rows of a 4 x 7 matrix Then show this matrix is invertible by multiplying it by itself Why does this make sense b Find the matrix E which scaled the fourth row of a 4 x 7 matrix by a 10 What about by a factor of a 10 Then show these matrices are invertible by multiplying them c Find the matrix E which performs row2 row2 7row What new row operation undoes this operation What is the corresponding matrix Show me that these two matrices are inverse to one another d Show me the two ways that you can perform the three elementary row operations I asked you you to consider in each part above swap first and second scale the fourth row by a factor and then the first combination both by actually performing the operations by hand and then by multiplying the corresponding matrices E E E A e Now since E E E A is the resulting matrix from the reduction algorithm it is some upper triangular matrix U so we have A E E E A U Find the inverse for E and multiple both sides on the left order matters to obtain E E E E A E E A E U Now repeat the same for E and E and finally multiply these inverse matrices together to find L such that A LU Congratulations you have worked out how row reduction is also a matrix factoring algorith