12. Let B = {(2, 1), (3, 4)} and D = {(1,1), (2,3)}, both of which are ordered bases for Z3.Let M = [id]B be a change of basis matrix. Which one of the following is true?4 64 13 3(a) M(b) М —6(c) M =112 11(d) М —4 1(e) M =2 65 5

12. Let B = {(2, 1), (3, 4)} and D = {(1,1), (2, 3)}, both of which are ordered bases for Z3. Let M = [id] be a change of basis matrix. Which one of the following is true? 4 6 4 1 3 3 (a) M = 1 (b) М — (c) M = 6 1 1 3 4 1 (d) м (е) М— 5 5 2 6

12. Let B = {(2, 1), (3, 4)} and D = {(1,1), (2, 3)}, both of which are ordered bases for Z3. Let M = [id] be a change of basis matrix. Which one of the following is true? 4 6 4 1 3 3 (a) M = 1 (b) М — (c) M = 6 1 1 3 4 1 (d) м (е) М— 5 5 2 6

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

Related questions

Q: b₁ b2 = = Multiply the following matrix / vector pair to obtain the vector b. 1 [ 3 ] [5] - [၁] =

A: Matrix multiplication

Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

Q: a1 For a fixed vector a = a2 E R³, we define the cross product as аз |a2x3 azx2 ахх%— a3X1 – a1x3…

Q: Consider the bases of R2 B1={(1,0),(1,3)} B2={(0,1),(1,1)} E={(1,0),(0,1)} Correspond M(Id)_B1_E (a…

A: To find a base change matrix from B1 to E, we need to find the linear combination of basis vector in…

Q: 2. (i) Let x, y be vectors in R?. Can one find a 4 x 4 permutation matrix P such that P(x y) = y ®…

Q: 2) Let T a d 11 la + 2b + (-6) c + 2d + (-18) e 2a + 5b+ (-14) c + 6d+(-46) e Then a basis for…

Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

Q: → Suppose TR³ R³ be a linear bronsformation whose standard matrix has the basis (o 1, 2), (2, 1…

Q: 9) please be clear with your answer, thanks!

A: Given the coordinate matrix of x relative to a (nonstandard) basis B for Rn, find the coordinate…

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R², where [1 C2 7 3 3 b1 b2 3 10 22 b7 what is…

Q: 40 0 0 1 0 3 20 1 -1 -1 -2 2-1 7 Where U is the reduced echelon form of A. 2 0 1 A = U [1200 -27…

Q: 6. Consider the equicorrelation matrix ... P p р -(15) A = р Find the explicit expressions of det(A)…

A: Given a equicorrelation matrix 1p...pp1...p......pp...1 To find the explicit expressions of det(A)…

Q: |a,6,d e а a, b, d E R}. S2x2 b d Do three matrices 1 A1 = 0 1 1 0 A2 = A3 1 0 - 1 | form a basis of…

Q: Determine whether or not the following sets S of 2 x 2 matrices are linearly independent s- {(; :)…

Q: Find a basis of Null(A), C(A), and C(AT) for each of the following matrices [1 2] 3 4 (i) A 1 2]…

Q: 5. Explain why three linearly independent vectors u,v,w in R³ form a basis for R³. (Hint: Consider…

A: Basis of a vector space : A non empty sub set S be a basis of a…

Q: 5. Consider the space {) a a + b+c= d : 2a + b = d a + b+ 3c = 0 H = CRª. C d (a) Find a matrix A…

Q: Q2/ Using Orthogonal Matrix 1 4 7, -8 4 If A = 4 prove that A- = A', A' being the transpose of A. 1

A: Solve by using the definition of the orthogonal matrix.

Q: (i.) Suppose ū € R¹ and 7 € R™ are non-zero (column) vectors. Show that the nx m matrix uuT has rank…

A: We know, rank of a matrix = row rank of a matrix = column rank of a matrix.

Q: Let A be a m x n matrix whose columns are vectors of R™. What is the smallest n must be so that…

A: Let A be the m×n matrix A=a11a12…a1na21a22…a2n⋮⋮⋱⋮am1am2…amnm×n that is the transformation matrix…

Q: A symmetric matrix satisfies M= M'. The set of 2 x 2 symmetric matrices S, with standard matrix…

Q: Find the specified change-of-coordinates matrix. Let B = {b₁,b2} and C = {₁, 2} be bases for R²,…

A: The change of coordinates matrix from B to C is calculated by " Write every basis elements of B as…

Q: Find the characteristic values and characteristic vectors of the matrix [8 − 6 2 − 6 7 − 4 2 − 4 3 ]

A: Consider the given matrix. A=8-62-67-42-43 Now, find the characteristic values.…

Q: Let ß = {b1, b2} and C = {c1, c2} be bases for R?. Find the change-of-coordinates matrix from ß to C…

Q: Write v as the sum of two vectors, one in Span (u₁} and one in Span (u2,U3,04). Assume that…

Q: Q5. Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is…

Q: (a) (BH) By direct multiplication, show that the listed vectors z; are eigenvectors for C1, and find…

Q: Let S = {(1,0, 1), (0, 1,0)} be two vectors in R³. Write the following vectors as a linear…

Q: V has bases B = (v1, v2, v3) and B' = (w1,w2, W3). If wi vị + 2v2 + 4v3, wz = 2v1 + 5v2 + 6v3, wz =…

A: Given that, B=(v1,v2,v3),B'=(w1,w2,w3) Given that,…

Q: Suppose A is the matrix for T: R3 → R³ relative to the standard basis. Find the diagonal matrix A'…

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal mama Da 15) 10-61…

A: The given matrix is 10-6-65

Q: Find A, B , A , B , and d(A, B) for the matrices in M2,2 using the inner product A, B…

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

12. Let B = {(2, 1), (3, 4)} and D = {(1,1), (2,3)}, both of which are ordered bases for Z3.
Let M = [id]B be a change of basis matrix. Which one of the following is true?
4 6
4 1
3 3
(a) M
(b) М —
6
(c) M =
1
1
2 1
1
(d) М —
4 1
(e) M =
2 6
5 5

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given.

VIEW

Step 2: Find the change of basis matrix M.

VIEW

Step by step

Solved in 2 steps with 14 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

( 8.) Let A be a nonsingular n x n matrix, then there are elementary matrices G1, G2, such that Gg .. G2 G A =1. GR . True / False :
Let B = {b1, {b1, b2} and C ={c1, c2} be two bases for IR“, where 1 b2 = 3 3 C1 3 b1 10 7 22 67 what is the value of b d a If the change-of-coordinates matrix from C to B is ? -36 26 О-35 25 -34
13. [R For each of the following 2 × 2 matrices, draw a picture to show Ae1, Ae2, Ab, where e and e, are the standard basis vectors in R? and where b = 2ej + 3e2. w 6 ) » (). (9), (3) () -2 0 0 2 -2 -2 4 -4 ), d) 0.7 0 -3 -1 -4
If the matrix of change of basis form the basis B to the basis B' is A = (³) O A. OB. 04 (3) 00 (12) 52 21 then the first column of the matrix of change of basis from B to B is:
9. Let and B 3 = {[B]-[-2]} = B' ={[2¹].[6]} be two ordered bases for R². Find the change of basis matrix [I]B'.
9. Given the bases B = {1+2t, 2+t} and C = {1-t, 2-3t} of P₁. Find the change of coordinates matrix Pc-B from B to C.
3. Find an example of a matrix that has Why can't this be a basis for the row space and the mullspace? 1. Explain why the vector v = H and as a basis for its row space and its column space. cannot be a row of A and also in the nullspace of A.
33. Prove that the row vectors of an n x n invertible matrix A form a basis for Rn.
11 - Which one is the transpose of matrix below? 2 1 A = (aj) 0 2 9 1 5 -5
7. (a) Consider the ordered basis ß = [1,1 +x, 1 + x + x²] for V = P₂ and F = R. Suppose is in P2 and you know these coordinates: [] = (1, 2, 3). Find the vector 7. (b) Let A be a 2 x 2 matrix and a be a real number. Prove that det (a A)=a² det(A)