Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, 21 + 4x2)*:\\ i). Find the matrix A representing L with respect to the standard basis for R?. i). Find the matrix B representing L with respect to S = {(1,1), (0, 1)}. ii). Find an invertible matrix P such that B = P-'AP. \

Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, 21 + 4x2)*:\\ i). Find the matrix A representing L with respect to the standard basis for R?. i). Find the matrix B representing L with respect to S = {(1,1), (0, 1)}. ii). Find an invertible matrix P such that B = P-'AP. \

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: 6-1) with T defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is…

Q: Find the matrix A' for T relative to the basis B'. T: R³ A' = R³, T(x, y, z) = (y + z, x - z, x -…

A: We have to Find the matrix A' for T relative to the basis B'.With the help of transformation and…

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

Q: et B = · 9, (x − 1)², 3x³) be an ordered basis for P3. Find the coordinate vector of (x) = 3x³ + 2x²…

A: Coordinate vector

Q: Let a11 a12 a13 A = a21 a22 a23 a31 a32 a33 3 x 3 real matrix and consider it as a linear map A: R³…

Q: Find the coordinate matrix of x in R" relative to the basis B'. [x]g' = B' = {(8, 11, 0), (7, 0,…

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

A: i just used the definition of matrix of A with respect to basis B'

Q: et L be the linear operator on R? defined by L(x1, x2) = (x1 + 2x2,3x1)* Find the matrix A…

Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

Q: Show that any isometry of R^n which fixes the origin is linear, and hence must be of the form f(x) =…

A: Introduction A square matrix is said to be an orthogonal matrix if…

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(-8, 9), (3, –2)}, x = (-37,…

Q: If the matrix of change of basis form the basis B to the basis B'is A= OA °;) 0⁰ (²) -3 2 then the…

Q: Find the standard matrix of the linear operator M: R2 R2 that first reflects every vector about the…

Q: Explain how fixing a basis v1, corresponding function in n variables of the form q(x1, · ·· , Xn) =…

Q: B=[(1, 2, 1)", (0, 1, -1)', (1, 1, 1)"] is an ordered basis for , C =[(1, 1)', (2, 3) '] is an…

Q: Find the matrix A' for 7 relative to the basis 8'. A' = T: R² R², T(x, y) = (x − y, 4y − x), B′ =…

Q: The second column of the matrix of change basis from the basis B = {u= (1,1,1); v = (1,0,1); w=…

Q: Show that if annxn matrix U satisfies (Ux)· (Uy) = x•y for all x and y in Rn, then U is an…

Q: Let V be a 2-dimensional vector space with two bases B and B' and let T be a linear operator on V.…

Q: a) Given matrices A and B are of the same size and invertible, and that the product AB is…

A: a)

Q: 0 1 1 (₁2) (₁) (1₂) Calculate matrix = = (A – AT)² and vector w = Bx. Then, Consider matrix A = X =…

Q: 5. Let B = {(1,0), (0,1)} and B' = a.). b.) {(2, 2), (1,4)} be ordered bases for R² and let v = (-3,…

Q: 1 - [5] and v₂ - [3]. = Let V₁ = [T(v₁)]B = ( be the matrix for T:R² R2 with respect to the basis B…

Q: Let J„ be the n × n matrix whose entries are all equal to 1, and let D(^1, ... , An) be the n × n…

A: The complete solutions are given below

Q: Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R22 and dim (R²x2); (2)…

A: Given be a linear space with all real matrices.Therefore .We need to find the basis of .The inner…

Q: Let f(x, y, z) = x°yz + 3z – 6xy + 2. - a) Compute the Jacobi matrix of f b) Compute the Hesse…

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

Q: (2 0 2 Consider the matrix A = 0 2 1. Find a Jordan matrix J and an 1 -2 0, invertible matrix Q such…

A: The given matrix: A= 2020211-20 The Jordan form of the matrix is given by finding the eigenvalues…

Q: Find a basis for the vector space (A E Rx4 tr(A) = 0} of 2x 2 matrices with trace 0. 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

Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, 21 + 4x2)*:\\
i). Find the matrix A representing L with respect to the standard basis for R?.
i). Find the matrix B representing L with respect to S = {(1,1), (0, 1)}.
ii). Find an invertible matrix P such that B = P-'AP. \
-1 -3
1 0
,P
2
-3
,B
4
A
%3D
3
-3
,B
4
-3
,P
2
-1
A
=
3
1 0
,P
6 7
2
2 0
-3
,B
4
A
3
,P
A
,B
1
2
-3
,B
4
1
1
A
,P

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 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

The third column of the change of basis matrix from the basis B={r= (1,1,1); v= (1,0,1); w= (0,1,1) } to the basis p'={r=(3,4,1); x= (3,0,1);t=(-4, - 1,- 2) is: caqe OA 1 1 0C (2 1 OD (-3
The second column of the matrix of change of basis from the basis B = {u= (1,1,1); v = (1,0,1); w= (0,1,1)} to the basis B'= {r=(3,4,1); s=(3,0,1); t= (1,2,0) } is: A. 2 1 B. 4 (4) OF (:) 0 (9) D. 1 ⁹9 1 E. 8)
V has bases B 2v1 + 5v2 + bv3, W3 = v1 + v2 + 5v3. (v1, v2, V3) and B' = (w1, w2, w3). If wi vi + 2v2 + 4v3, W2 = Determine the change of basis matrices, PgB and Pg¬B'-
Let {v1, v2, . .. , vn} be an orthogonal set in R" with respect to the Euclidean inner product. Let A be the n x n matrix with row vectors v1, v2, ... , Vn. b) What extra condition(s) do we need from the vectors v1, v2, ..., Vn so that the matrix AAT is an identity matrix? Justify your answer!
6) PLEASE ANSWER EACH QUESTION, THANKS.
Consider the bases v₁ = (1,0)¹, v₂ = (0, 1) and v₁ = (2, 1), v₂ = (1,3)¹ of R². The transition matrix from the basis {V₁, V₂} to the basis {v₁, v₂} is
Consider B={1,x,x^2} and B'={1+x,1-x^2,2} Find the change of basis matrix 1.P from Bto B' 2.Q from B' to B Further find the relation between P and Q
Write down anxn matrix A such that Cond(A) =1, but determinant(A) → 0 as n → ∞.
Find the coordinate matrix of x in R" relative to the basis B. B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)), x = (-4, 19, -8) [x] = 000 11 It 7