Unformatted text preview: ï£« ï£¬ ï£¬ ï£¬ ï£¬ ï£ 12 3125 1214 199 2220 314 914 15 ï£¶ ï£· ï£· ï£· ï£· ï£¸ (b) Solve the following systems of linear equations using Cramerâ€™s rule. x 1x 2 +4 x 3 =26 x 1 +3 x 2 + x 3 = 2 x 1x 2 + x 3 = 3 . 3. (10%) Let E be an elementary matrix. Show that, for any square matrix B , that det( EB ) = det( E )det( B ) . (Prove directly without using the results of Theorem 4.7.) 4. (10%+4%) Let A * be the Hermitian of the matrix A deÂ±ned by ( A * ) i,j = A j,i for all i , j , where A j,i is the complex conjugate of A j,i (a) Prove that det( A ) = det( A ). (b) A matrix A âˆˆ M n Ã— n ( C ) is called unitary if AA * = I . Prove that, if A is a unitary matrix, then  det( A )  = 1. 1...
View
Full Document
 Spring '11
 EE
 Linear Algebra, 10%, 6%, 4%, Î´

Click to edit the document details