Question A particular matrix A in block 3 x 3 form (i.c., 3 row blocks, and 3 column blocks), is given underneath. The matrix L is full-rank. I and O represent the identity matrix and the all-zero...

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Extracted text: Question A particular matrix A in block 3 x 3 form (i.c., 3 row blocks, and 3 column blocks), is given underneath. The matrix L is full-rank. I and O represent the identity matrix and the all-zero matrix of the correct orders. Determine the algebraic forms of the Schur complements S2 and S3, so that the given LDU and UDL factorizations (of A, and A-1 respectively) hold. A11 and A22 are square non-singular matrices. By substituting the expressions for S2 and S3 in the expression(s) below show that they are correct by multiplying the block matrices to retrieve A. You must NOT use any numerical examples in this assignment -this is purely algebraic work. I ATA12 Au A12 L A21 A22 O LT I A11 ATL -S,'A21 AL I A= I I LT A -L" AA12S, I O S3 I -A A12 -Aj A12S, 'A21 AL- AL A JI I S'A21 AL A21 AT - A21 ATLT AA12S, - L" A LAT'A128, » A = I I I