solution7

# solution7 - M341 Homework Solution 7 Section 3.2 2(b A = 18...

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Unformatted text preview: M341 Homework Solution 7 Section 3.2: 2(b) : A = 18 − 9 − 14 6 − 3 − 5 − 3 1 2 (III) ⇒ − 3 1 2 6 − 3 − 5 18 − 9 − 14 (II) ⇒ − 3 1 2 − 1 − 1 1 = T Since type (III) row operations change the sign of the determinant and type (II) row operations have no e ect on the determinant we have | A | = − 1 | T | = − ( − 3)( − 1)(1) = − 3 . 2(d) : A = − 8 4 − 3 2 2 1 − 1 − 1 − 3 − 5 4 2 − 4 3 − 1 (I), P = -1/8 ⇒ 1 − 1 / 2 3 / 8 − 1 / 4 2 1 − 1 − 1 − 3 − 5 4 2 − 4 3 − 1 (II), P = -1/8 ⇒ 1 − 1 / 2 3 / 8 − 1 / 4 2 − 7 / 4 − 1 / 2 − 13 / 2 41 / 8 − 3 / 4 − 3 9 / 4 − 1 / 2 (I), P = -1/16 ⇒ 1 − 1 / 2 3 / 8 − 1 / 4 1 − 7 / 8 − 1 / 4 − 13 / 2 41 / 8 − 3 / 4 − 3 9 / 4 − 1 / 2 (II), P = -1/16 ⇒ 1 − 1 / 2 3 / 8 − 1 / 4 1 − 7 / 8 − 1 / 4 − 9 / 16 − 19 / 8 − 3 / 8 − 5 / 4 (I), P = 1/9 ⇒ 1 − 1 / 2 3 / 8 1 / 4 1 − 7 / 8 − 1 / 4 1 38 / 9 − 3 / 8 − 5 / 4 (II), P = 1/9 ⇒ 1 − 1 / 2 3 / 8 1 / 4 1 − 7 / 8 − 1 / 4 1 38 / 9 1 / 3 = T Since type (I) row operations multiply c to the determinant and type (II) row operations have no...
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solution7 - M341 Homework Solution 7 Section 3.2 2(b A = 18...

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