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Unformatted text preview: Review Problems for Exam One 1. Represent the following system of equations by an augmented matrix, reduce this matrix to upper triangular form by Gaussian Elimination and then use back substitution to find the solution. x + 2 y + 4 z = 0 3 x + 8 y + 8 z = 2 2 x + 6 y + 9 z = 7 2. Put the matrix A = 1 2 0 0 3 2 4 1 3 0 2 4 2 3 1 into reduced row echelon form and then give the general solution to the equation A→ x =→ 0 and express in parametric form. 3. Let A be an m × n matrix, where m < n . Explain why the homogeneous system of equation A→ x =→ 0 has a nontrivial solution. 4. Let A be an m × n matrix with entries a ij , let B be an n × r matrix with entries b ij , and let C be an n × r matrix with entries c ij . Prove that A ( B + C ) = AB + AC . 5. Prove that if A is invertible, then A T is also invertible. 6. Suppose that→ u is a solution of A→ x =→ 0 and that→ v is a solution of A→ x =→ c . Explain carefully why 2→ u +→ v is a solution of...
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This note was uploaded on 12/27/2011 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.
 Spring '09
 RUDYAK

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