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Unformatted text preview: 1 2 x 1 + 4 x 2 + 3 x 3 + 3 x 4 = 3 x 1 + x 2 + x 3 + x 4 =1 (10 points) Problem 4. By using the Cramer’s rules solve the linear system: x 1 + x 2 + x 3 = 2 x 1 + x 2x 3 = 3 x 1x 2x 3 = 4 No other method will be accepted (10points = 5 for Cramer’s formulas + 5 for calculations) 1 Problem 5. 1) Compute the determinant of the matrix: A = 3 21 1 6 3 24 (5 points). Is A invertible and why? (3 points) 2) Give the matrix of cofactors for A (5 points). What is the adjoint or adjugate matrix? (3 points) give the adjugate matrix of A (2 points). What is the inverse of A (formula: 5 points, calculations: 2 points). 3) Use the inverse of A to solve: ( 5 points.) 3 x 1 + 2 x 2x 3 = 6 x 1 + 6 x 2 + 3 x 3 = 30 2 x 14 x 2 = 8 2...
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 Spring '11
 SECKIN
 Linear Algebra, Determinant, Matrices, Invertible matrix, Cramer

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