# Differential Linear Algebra Questions Assignment Help

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Name Math 264 Summer 2021 Homework Set 6 Show all work! 1. Determine the rank of the matrix A. (4 pts.) 01 2 31 A = @ 4 8 12 A 2 4 6 . 2. Let AX = B be a consistent linear system with 11 equations and 7 variables. If the solution of the system contains 2 free variables, then what is the rank of the coecient matrix A? (2 pts.) 1 3. Calculate the determinant of the matrix A using cofactor expansion. (4 pts.) 0 1 3 0 B 2 0 4 A=B @ 1 0 1 3 4 0 2 21 1C C 0A 2 4. Let 0a a a 1 1 2 3 A = @ b1 b2 b3 A c1 c2 c3 and suppose that det A = 10. Determine det B if 0 4b 4b2 4b3 1 1 5a2 5a3 A B = @ 5a1 c1 + 3a1 c2 + 3a2 c3 + 3a3 (3 pts.) 3 5. Use an inverse matrix to solve the system consisting of the following equations. (3 pts.) 7x 3y = 36 and 4x + 2y = 2 6. Find A 1 if it exists. (4 pts.) 01 4 3 1 A=@ 3 0 5 A 2 1 4 4

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