# review3 - Math 375 Review problems III Do the following...

This preview shows pages 1–2. Sign up to view the full content.

Math 375 – Review problems III Do the following problems from the book. 3.6: 4a, c, 6. 3.11: 5. 3.17: 1c, 2c, 3c. 4.4: 2, 5. 4.8: 4, 5, 6, 8, 11. Review the handout on determinants to do No. 9 in 4.8. or come up with your own proof. 5.11: No 1, 5, 7, 8, 12. 1. Let A = 2 - 1 0 5 0 0 2 0 0 3 7 4 1 2 5 3 . Evaluate the determinant of A . b) Is A invertible? If so compute the determinants of ( A t ) - 1 and A 5 (do not compute A 5 ). c) Let x R 4 be the solution of 2 - 1 0 5 0 0 2 0 0 3 7 4 1 2 5 3 x 1 x 2 x 3 x 4 = 2 0 - 6 - 4 Determine the coordinate x 3 without using Gaussian elimination and without com- puting the inverse A - 1 . 2. i) Find the 2 × 2 matrix A = ± a b c d ² which satisﬁes A ± 2 3 ² = ± 8 12 ² , A ± 1 1 ² = ± 1 1 ² . (ii) Find A 1000 . 3. Let u 1 = 1 1 1 , u 2 = 0 - 1 1 , u 3 = 2 - 1 - 1 . Find the 3 × 3 matrix A which satisﬁes Au 1 = 2 u 1 , Au 2 = 4 u 2 , Au 3 = 3 u 3 . (Observe that the

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

### Page1 / 3

review3 - Math 375 Review problems III Do the following...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online