I have a question that requires me to "write the inverse of matrix A as a product of 4 elementary matrices" How would I go about doing this? I have already written A as a product of elementary matrices does this help at all?
2007-10-20 13:43:25 · 3 answers · asked by Bikki 3 in Science & Mathematics ➔ Mathematics
What is matrix A? Is it 3-by-3?
2007-10-20 13:47:05 · answer #1 · answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6 · 0⤊ 0⤋
Yes, it does. Finding the inverse of an elementary matrix is easy, all you need to do is write the matrix for the inverse operation (e.g. if E is the elementary matrix for adding k*row 1 to row 3, then E⁻¹ is the elementary matrix for adding -k*row 1 to row 3). And if ABCD are any four invertible matrices, then (ABCD)⁻¹ = D⁻¹C⁻¹B⁻¹A⁻¹ (note order). So find the inverses of each of the four elementary matrices, write them down in reverse order, and that's the inverse of your matrix as a product of elementary matrices.
2007-10-20 13:53:07 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
sorry, i have forgotten about inverse.
2007-10-20 13:59:03 · answer #3 · answered by duhibowl 3 · 0⤊ 0⤋