3 10 08 2 132 1 8 0 1 8 0 0 1 4 8 1 that is

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: Find the coordinate vector of p (i) Consider p ,p , 2 . relative to B. 3 for standard basis C = 1, , p 101 10 1 10 1 101 Then 0 2 2 ~ 0 2 2~0 1 1 ~ 0 1 1 and the columns form a basis for 330 03 3 01 1 002 the IMT. is isomorphic to , so the corresponding polynomials form a basis for . (ii) Working in coordinates relative to the standard basis again, b b b 1 101 022 330 2 10 3~0 2 1 03 1 2 3 0 1 2 0 3~ 5 0 1 1 1 1 100 ~0 1 0 001 So p 23/12 19/12 1/12 2 101 3 011 2~ 5 002 3 23/12 19/12 1/12 p by p, so 2 101 3 011 2~ 1 001 6 2 3 2~ 1 12 Part IV. True/false questions [2pts each]: Write “True” or “False” in the blank. No justification is needed. TRUE 1. If and are similar matrices, then det = det . , then there is a 3 x 3 matrix A such that H = Col A. TRUE 2. If H is a subspace of FALSE 3. If A is m x n and rank A = m, then the linear transformation TRUE 4. If 0, then det is an n x n matrix and x x is one-to-one. 0. FALSE 5. An n x n matrix with n linearly independent eigenvectors is invertible. FALSE 6. A plane in is a two-dimensional subspace of TRUE 7. For a 5 x 7 matrix A, dim Nul A . 2. FALSE 8. Row operations on a matrix can change the null space of the matrix. TRUE 9. The matrix 5 0 0 0 0 3 2 0 0 0 4 1 6 0 0 7 0 0 3 0 8 2 1 is diagonalizable. 4 1 FALSE 10. If A is a 3 x 3 matrix, then det 3A = 3 det A....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online