**C: An Example of Diagonalisation**Let $ T $ be the operator of $ \mathbb{C}^3 $ with matrix \[M = \begin{pmatrix}1 & 2 & 1+i \\0 & i & 2i-1 \\0 & 0 & -i\end{pmatrix}.\]2) Find the matrix of $ T $ in the basis $ (e_1, e_2, e_3) $.

Answered: Image /qna-images/answer/9b277175-0175-4512-8d3c-6316c89b6e27.jpg

Answered: 1 C: An example of diagonalisation: Let…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Define 0 1 B. - 13 V3 = 0 (Here, a, b, c, d are some unknown constants.) Assume that v3 is nonzero and is orthogonal to both vi and v₂. Also, let A be a 2 x 4 matrix whose row vectors are v₁ and v2, that is, V1 = (a) v3 is in Col(A). (b) v3 is in Nul(A). (c) v3 is in Row(A). A = V2 = 1 -1 1 0 -1 0 1 Mark each of the following statements as: (i) must be true, (ii) must be false, or (iii) may or may not be true.
Let ß = and = -3 are bases for R². a. Find the change-of-coordinates matrix from & to B. b. If (s), - 3 then find x 2 أقصي حجم ل لملف: 50 ميغا بایت PDF 国* 因 ...Note_MATH14 r .Part B FINAL EXA FUJITSU
Let A be a 3x3 matrix such that Assume that the vector V = E -2 is a solution of the matrix equation 3 Enter the vector V₁ in the form [C₁, C2, C3]: -12 12 -24 Find three vectors V₁, V₂, V3, different from V, which are also solutions of this equation. Enter the vector V₂ in the form [C1, C2, C3]: Nul (A) = Span (3) ED Enter the vector V3 in the form [C1, C2, C3]: Ax=
Matrix A = a11 a12 a21 a22 a31 a32 B = b1 b2 C = c1 c2 c3 Find C*A. Transpose C*B.
Let B = and C = be bases for R. Find the change-of-coordinates matrix from B to Cand the change-of-coordinates matrix from C to B. - 1 1 C1 = - 2 b, = b, = 3. C2 2 Find the change-of-coordinates matrix from B to C P = (Simplify your answers.) C-B
deo 1 Q A T N @ 2 siks 394 W Identify the orthogonal matrix. S O X H command A = O w # A = O A = 20 F3 E D 12 12 - [1] 0 -[₁ C. 4 1 I $ ²333 F4 R 1 F 130 01/3 cals 25 % V 121 F5 lo 3 T G A 6 MacBook Air B F6 Y & 7 H 44 F7 U N M 8 J D-II FB ( M 9 D T K FO O ) O V. L F10 - P A. 4 20 F11 i Time Re Attempt d 1 Hour, - = [ 1 ? command option
The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below. Standard basis S= (₁, ₂) 4 a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates. [id] = id= -2 b Find the change of basis matrix from custom C-coordinates to standard S-coordinates [id] = -1 -1 -1 c. Find the change of basis matrix from B-coordinates to C-coordinates -3 -1/12 1/4 d. Find the change of basis matrix from C-coordinates to B-coordinates. 3 2 1 -1 -2 -9 b2 -3-2-1 82 el bl 1 2 3 b1 X Custom basis B = {b₁,b₂) |id|s [id Standard basis S= (0₁,0₂} a 3 2 1 -1 -2 -9 c2 -3 -2 -1 G2 62 217 el [id] ↑ cl 12 2 3 61 H x Custom basis C (C₁, C₂)
1 C: An example of diagonalisation : Let T be the operator of C³ with matrix M = 0 1) Find 3 vectors e₁ e2 e3 satisfying the equations : { 2) Find the matrix of T in the basis (e₁,e2, e3). 3) Use this to find 74 with as little computation as possible. T(e₁) = e₁ T(e₂) = ie₂ T(e3 = -iez 2 1+i i 2i1 0 -i
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. A = 2 -2 4 10 - 16 16 2 -26 40 4 -8-2
Use the definition of Ax to write the vector equation as a matrix equation. 3 5 [H³H-HAD +23 3 3 -4 +Z4 5 -1 The vector equation written as a matrix equation is 1

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

1 C: An example of diagonalisation: Let T be the operator of C3 with matrix M = 0 0 2) Find the matrix of T in the basis (e₁, €2, €3). 1+i 2i 1 2 i 0 -i