Answered: Find the matrix of the linear…

Find the matrix of the linear transformation T from R? R?, where T([1, 0]) = [1, -2], and T([2, 1]) = [2, 3] (Note: matrix A = [T([1, 0]), T([0, 1])] ). 1 (b) -2 3 2 1 (a) 1 (c) -2 7 1 -2 (d) 3

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: Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 +…

A: Here we will find matrix of linear transformation

Q: Write the matrix corresponding to the following linear transformations. 2x1 – x2 – x3 Yı Y2 = 3x3 Y3…

A: Given that : y1 = 2x1-x2-x3y2 =3x3y3 =x1+x2

Q: Suppose T: R³ → R2 is a linear transformation with T(x1, x2, 3) = (-10x2, -5x1+11x2 - 7x3). Find the…

Q: 3. Consider the linear transformation T: R R given by T(#1, 12, T3) = (21 + 303,-22- 4x3, 201 +…

Q: 2. Let T: R³ R³ be the linear transformation given by x1 + x2 + x3 +((:))-[ T X2 2x1 x2 + 7x3 -4x₁ +…

Q: M = Find the matrix M of the linear transformation T: R³ → R² given by 3 X1 (E)- = X3 T -9x1 - x2 +…

Q: Find the matrix M of the linear transformation T : R3 → R2 given by () [ = M: T -9x1 + x2 + (-4)x3…

Q: Find a 3 by 3 matrix that scales the point (x,y,z) by 2 in the x direction and 4.5 in the direction,…

Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

Q: Consider a linear transformation T from R³ to R2 Find the matrix A of T. A = for which CD-· -· D-4 0

A: Here for the given transformation we have to find the matrix A of T.

Q: Let B=(b₁,b₂), C={C₁,C₂), be bases for R² b₁ = (-1,2), b₂ = (1, -1), C₁=(1,2), C₂ = (1,1) Find the…

Q: The cross product of two vectors in R³ is defined by b₁ a₂b3 - a3b₂ 8-0-6-3 b₂ a3b₁ - α₁b3 b3 a₁b₂ -…

Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R² →R² first reflects…

A: Given: T:ℝ2→ℝ2 is a linear transformation which first reflects points through the line x2=x1, then…

Q: Suppose that T is a linear transformation from R2 to the space of 2 × 2 matrices which satisfies:…

Q: Suppose T: R² R² is a linear transformation that first reflects points across the ₁-axis and then…

Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

Q: A B -2 -2

Q: 6. (BH) For each of the following linear transformations, determine the kernel, the range, and write…

Q: Given the following system of linear equations: 3x, + 4x, 1 %3D 2x, 2x, + = -1. 2x, 2x, + 4x, = 0…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

Q: Determine a matrix A that describes the following linear transformation. T([*]) = [2x+³] 3y

Q: Let T: R² → R2 be the linear transformation which first reflects in R² about the line y = x, and…

Q: 2. Determine whether the matrix transformation T(x,y)=(3x,-5.x) is one- to-one.

A: T is not one-to-one.Explanation:

Q: With bases V1, V2, V3 andw1, w2, W3, suppose T(v1) = w2 and T(v2) = T(v3) = w1 + w3. T is a linear…

Q: M = Find the matrix M of the linear transformation T : R³ → R² given by X1 X3 = 8x₁ − x₂ + (−2) x3…

Q: Let A be a 8×7 matrix. What must a and b be if we define the linear transformation by T: R^a → R^b…

Q: [102] 6. Find the kernel of the linear transformation whose standard matrix is B= 215. [237]

Q: Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0, 1) → (4, –1). (a) What is…

A: Follow step 2.

Q: Find the standard matrix for the linear transformation T. TN, Y, 2) - (x+ 1,x-Y. 2-x)

Q: M = Find the matrix M of the linear transformation T: R³ → R² given by * ((:D) - T = 2x1x₂ + (-7):…

Q: 1. (a) Find the matrix P that multiplies every vector (x, y, z) E R³ to produce the vector (3x+2y+z,…

A: What is Linear Transformation: A function from one vector space to another that respects the…

Q: 2. Write the following functions in matrix form: (a) f(x1,x2, X3) = (x1 + 2x3, x1 + 3.x2 – x3, x1)…

A: Given the function is a fx1,x2,x3=x1+2x3, x1+3x2-x3, x1 In a matrix form…

Q: Construct a 4×3 matrix A and vectors ~b and ~c in R4 so that ~b is in the range ofthe linear…

Q: The matrices 0 4₁ = [10], 4₂ = [8] · A3 rm a basis for the linear space V = R2x2. Write the matrix…

A: The matrix representation of a linear transformation is obtained by expressing the transformation of…

Q: Which of the following matrices can be used for a single transformation of translation of a line…

A: In this question, the vector which provides the transformation of translation of a line is…

Q: If X and Y are two full column-rank matrices of rank p, find all matrices A for which R(A) = R(X)…

A: Here given that are two column rank matrices of rank so that where .Obviously .From above…

Q: Consider the matrix A = show that the product L(X)=Ai is a linear transformation, where žER*.

Q: [2v1 5. (a) Let T be a linear transformation such that T What is its matrix? (b) Let T be a linear…

Q: 6. Let T be a linear transformation from R to R?given by T(x, x2x3) = (3x1 - 5x2 + X3, X1 + 6X3)…

Question

Find the matrix of the linear transformation T from
R? R?,
where T([1, 0]) = [1, -2],
and T([2, 1]) = [2, 3]
(Note: matrix A = [T([1,0]), T([0, 1])] ).
1
(a)
1
(b)
1.
(c)
-2
1
-2
3
-2
1
(d)
0.
3

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Transformation$

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

Find the standard matrix for the linear transformation T(1, 9) — (2а — Зу, т — у, у — 4г) -3 1 -1 1 1 -4 2 1 -4 -3 -1 1 -3 -1 2 1 1 -3 -1 2.
Find the standard matrix of the linear transformation. -y x + 4y 6x 2y
Find the B-matrix for the transformation xAx when B= (b,, b,, ba). -8 - 72 - 18 -3 4 A = 1 16 5 |, b1 1, b2 1 b3 = -4 - 68 -21 4 4 The B-matrix is
True or false The linear transformation of vectors to Xa = 0 has many solutions if matrix X is less than full rank.
Complete the matrix representation for the linear transformation T : P2 → P2 given by Т(ая? + ba + c) 3 (ба — 3b + 2с)2? + (5а — 36 + 3c)x + (-За + 2b — 2с). Ex: 5 a
f and g are linear transformations which in matrix form are (0 -4) and (3 3) (2 1) (-5 -4) What is the image of the point (-1,1) under the composite transformation g o f?
Find the matrix of the linear transformation T from R2 - R² where T([1, 0]) = [1, –2] and T([2, 1]) = [2, 3] %3D (Note: matrix A = [T([1, 0]), T([0, 1])] 1 -2 (a) 1 (b) 1 (c) -2 (d) -2 3 7 3 Ob a C
Suppose T is a linear transformation, where (1, 0, 0) T(u) T(7) (0, 1,0) W (0,0,1) T(w) Then I can be represented by the matrix ū V = = = T= = = = (5, -3, -2) (-2,-1,0) (0,5, 4)
Suppose T transposes every 2 by 2 matrix M. Try to find a matrix A which gives AM = MT. Show that no matrix A will do it. To professors: Is this a linear transformation that doesn't come from a matrix? The matrix should be 4 by 4!
3x₁ - x₂ [-x₁ + x₂] 1. (i) Show that 7 ([x₂]) = [³ T (ii) Find the matrix representation is a linear transformation. of T relative to the standard basis.
The cross product of two vectors in R³ is defined by Let ✓ = A = [1] 8 . Find the matrix A of the linear transformation from R³ to R³ given by T(x) = × đ. a2 X b₁ b₂ b3 = [a2b3-a3b₂] | a3b1 — a1b3 [a1b₂-a2b₁]