1.4soln

# 1.4soln - Solutions to problems from section 1.4 7 3 2 1 6...

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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 0 5 3 , b = 0 1 - 1

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Solution: 1 2 1 0 - 3 - 1 2 1 0 5 3 - 1 NR 2 = R 2 +3 R 1 -→ 1 2 1 0 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 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 -→ 1 0 0 3 5 0 1 0 - 4 5 0 0 1 1 .
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