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Given that AX(D + BX) - C for X Assuming that all matrices are non and invertible as needed, so, At exists. Now AX (Dr BX) +- e (multiplying » (AT A/X (O+BX) ta Ate by At both.
2) IX (D+BX) + = Ate side) > X [since A.At=I (O+B) t = Ate xx Cor BX) = XAtc ( with x) I. (D+BX) = xtata * D + Bx) = xtate -> (xYA+C) CD+ BX3 = (D+x) (O+B) 9 (XHATC DH (XHAT CBX) = I XXMATCD + X XMATCBX = X by x both ... AICD + side ] At CBX = X (multiplying
- AtcD = X - At CBX AT CD = X (I- ATCB) - CATED) (I - Ate B)+= X(I - AC3) (I - ACB)4 - CATCD) (I - ATCB) = X. I . X = CATCD) (AI - ATCB) -
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