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...Math special types of matrices and partitioned a denitions an n matrix is diagonal if aij whenever i j scalar it whose elements are all equal the identity denoted in entries to examples b o claim for any m ain ima k y notation we use denote product square with itself times p q pq question does ingeneral upper triangular lower t real symmetric skew note as consequence denition both must be addition forces zero since aii c d submatrices formed by deleting some but not its rows or columns submatrix original example let delete second column third row obtain form subdivide given into adding dotted lines between portion augmented representing linear system another singular nonsingular invertible there such that ab ba no exists say noninvertible exist silly will see other non trivial theorem inverse unique proof find following provided they suppose then also homework using solve equations unknowns notice x therefore thus this mind can nding coecient right multiplying nd solution...