Math254OldFinalSols

# Math254OldFinalSols - FINAL SOLUTIONS MATH 254 SUMMER 2001...

This preview shows pages 1–3. Sign up to view the full content.

FINAL - SOLUTIONS MATH 254 - SUMMER 2001 - KUNIYUKI 1) Find the inverse of the matrix A = È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 040 100 002 . (8 points) Idea: AI IA [] Æ - 1 . 010 001 È Î Í Í Í ˘ ˚ ˙ ˙ ˙ È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 14 0 0 00 1 2 / / È Î Í Í Í ˘ ˚ ˙ ˙ ˙ RR 12 ´ 1 4 22 Æ 1 2 33 Æ So, A - = È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 1 1 2 / / 2) Find the determinant of the matrix A = -- 000 3127 62 31 5004 2 . (10 points) Let's expand along the first row, since it has the most zeros. Its only nonzero entry is the " 2 "; the corresponding sign from the sign matrix is "-" [or you could observe that - () =- ++ 111 1 14 5 ij ]. To get the submatrix for the corresponding minor, we delete the row and the column containing the " 2 ". 0002 5 312 3 500 2 3 =- () ( ) -= - - from sign matrix {

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

View Full Document
Let's expand along the third row, since it has the most zeros. Its only nonzero entry is the " 5 "; the corresponding sign from the sign matrix is "+" [or you could observe that - () =- () = ++ 111 1 31 4 ij ]. To get the submatrix for the corresponding minor, we delete the row and the column containing the " 5 ". -- = - - Ê Ë Á ˆ ¯ ˜ =- - - 2 312 62 3 2 5 12 23 253 4 257 70 500 3) Let v 1 = (1,2) and v 2 = (3,5). Express (-7,-9) as a linear combination of v 1 and v 2 . There should be no unknowns in your final expression. (10 points) Solve vv 7 9 - - È Î Í ˘ ˚ ˙ for c 1 and c 2 , the weights for the linear combination. 13 25 7 9 - - È Î Í ˘ ˚ ˙ 01 7 5 - - È Î Í ˘ ˚ ˙ 10 8 5 - È Î Í ˘ ˚ ˙ 8 5 - È Î Í ˘ ˚ ˙ RRR 212 2 121 3 RR 22 So, c 1 = 8 and c 2 = -5. - - È Î Í ˘ ˚ ˙ 7 9 85 4) The vectors x , y , and z are three vectors in R n for some fixed n .
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/08/2011 for the course MATH 254 taught by Professor Howard during the Spring '09 term at Mesa CC.

### Page1 / 7

Math254OldFinalSols - FINAL SOLUTIONS MATH 254 SUMMER 2001...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online