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Unformatted text preview: Solutions to problems from section 1.4 6. Write the matrix equation 7 3 2 1 9 6 3 2 bracketleftbigg 2 5 bracketrightbigg = 1 9 12 4 as a vector equation. Solution: 2 7 2 9 3  5  3 1 6 2 = 1 9 12 4 . 10. Write the system first as a vector equation, then as a matrix equation. 8 x 1 x 2 = 4 5 x 1 + 4 x 2 = 1 x 1 3 x 2 = 2 Solution: Here’s the vector equation: x 1 8 5 1 + x 2  1 4 3 = 4 1 2 . Here’s the matrix equation: 8 1 5 4 1 3 bracketleftbigg x 1 x 2 bracketrightbigg = 4 1 2 . 12. Write the augmented matrix for the linear system corresponding to the matrix equation A x = b . Then solve the system and write the solution as a vector. A = 1 2 1 3 1 2 5 3 , b = 1 1 Solution: 1 2 1 3 1 2 1 5 3 1 NR 2 = R 2 +3 R 1→ 1 2 1 0 5 5 1 0 5 3 1 NR 3 = R 3 R 2→ 1 2 1 0 0 5 5 1 0 0 2 2 NR 3 = 1 2 R 3→ 1 2 1 0 0 5 5 1 0 0 1 1 NR 2 = R 2 5 R 3→ 1 2 1 0 5 0 4 0 0 1 1 NR 1 = R 1 R 3→ 1 2 0 1 0 5 0 4 0 0 1 1 NR 2 = 1 5 R 2→ 1 2 0 1 0 1 0 4 5 0 0 1 1 NR 1 = R 1 2 R 2→...
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This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.
 Fall '08
 AXENOVICH

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