selected10.5

selected10.5 - Solutions to requested homework problems...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions to requested homework problems from section 10.5 in the course notes: __________________________________________________________________ 0 3 5 4 1 0 2. Given A = , and B = , compute 3 A − 2 B. −2 3 −2 1 2 6 Solution: 0 9 15 8 2 0 3A = and 2 B = −4 6 −4 . By subtracting corresponding entries, we 3 6 18 9 − 2 15 − 0 −8 7 15 0−8 obtain 3 A − 2 B = = . 3 − ( −4) 6 − 6 18 − ( −4) 7 0 22 __________________________________________________________________ 5. Given 4 1 0 3 5 and C = 6 2 , compute AC − 3 I2 . A= 1 2 6 −2 3 Solution: 4 1 0 3 5 3 0 0 + 18 − 10 0 + 6 + 15 8 21 AC = 6 2 = 4 + 12 − 12 1 + 4 + 18 = 4 23 , and 3 I2 = 0 3 . 1 2 6 −2 3 8 − 3 21 − 0 5 21 Subtracting corresponding entries, we obtain AC − 3 I2 = . = 4 − 0 23 − 3 4 20 __________________________________________________________________ 1 1 1 9. Find the inverse of the matrix A = 3 2 −1 . 3 1 2 Solution: (The two column method below helps to reduce careless copying or arithemtic errors. ) Sequence of row equivalent matrices 1 1 1 1 0 0 −3r1 + r2 = R2 3 2 −1 0 1 0 → 3 1 2 0 0 1 “Scratch” −3r1 −3 −3 −3 −3 0 0 r2 3 2 −1 0 1 0 R2 0 − 1 −4 −3 1 0 Sequence of row equivalent matrices 1 1 1 1 0 0 −3r1 + r3 = R3 0 −1 −4 −3 1 0 → 3 1 2 0 0 1 1 1 0 0 1 1 r1 + r2 = R1 0 −1 −4 −3 1 0 → 0 −2 −1 −3 0 1 1 0 −3 −2 1 0 −2 r2 + r3 = R3 0 −1 −4 −3 1 0 → 0 −2 −1 −3 0 1 1 0 −3 −2 1 0 3r3 + rR1 = R1 0 −1 −4 −3 1 0 → 0 0 7 3 −2 1 7 0 0 −5 1 3 4 r3 + 7r2 = R2 0 −1 −4 −3 1 0 → 0 0 7 3 −2 1 “Scratch” −3r1 −3 −3 −3 −3 0 0 r3 3 1 2 001 0 −2 −1 −3 0 R3 r1 r2 11 1 100 0 −1 −4 −3 1 0 R1 1 0 −3 −2 1 −2r2 r3 R3 0 0 7 3 7 1 7 1 7 2 − 7 3 7 4 − 7 1 7 . -2 1 3r3 0 0 21 9 −6 3 7 r1 7 0 −21 −14 7 0 R1 70 0 −5 1 3 4r3 0 0 28 12 −8 4 7r2 0 −7 −28 −21 7 0 R2 0 −7 0 − 9 −1 4 7 0 0 −5 1 3 0 −7 0 −9 −1 4 → 0 0 7 3 −2 1 0 0 −5 7 9 10 7 0 13 0 0 2 8 6 −2 0 0 −2 −1 −3 0 1 1 r1 = R1 7 1 − r2 = R2 7 1 r3 = R3 7 2 1 0 0 1 − 5 7 9 So A−1 = 7 3 7 1 7 1 7 2 − 7 3 7 4 − . 7 1 7 ...
View Full Document

Ask a homework question - tutors are online