Let a and B be the standard bases for R" and R" respectively. Foreach of the following linear transformations T; : R² → R", compute thematrix [T;%-2ab()(a) T1 : R² → R³, TЗа + 46a() - (*:)(C)(C)(2а + 3b —.a +b(b) Т, : R3 — R?, T,b(c) T3 : R³ → R', T3= (2a + b – 3c).(d) T4 : R" → R", T4

By bartleby rules, only first three sub parts have been answered Given linear transformation is…

Let a and B be the standard bases for R" and R" respectively. For each of the following linear transformations T; : R" → R", compute the matrix [T;%. (6) - (*-) () - (*:) () 2а —b (a) T1 : R? → R³, T1 За + 4b a 2а + 3b — (b) T2 : R³ → R², T2 %3D a + b (c) T3 : R³ → R', T3 = (2a + b – 3c).

Let a and B be the standard bases for R" and R" respectively. For each of the following linear transformations T; : R" → R", compute the matrix [T;%. (6) - (-) () - (:) () 2а —b (a) T1 : R? → R³, T1 За + 4b a 2а + 3b — (b) T2 : R³ → R², T2 %3D a + b (c) T3 : R³ → R', T3 = (2a + b – 3c).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...

See similar textbooks

Related questions

Q: (a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor- mations L₁ and L2,…

A: (a)Two Linear transformations are mentioned:.Thus the matrix for the transformation is given by and…

Q: (b) B={(-1,3), (2, -1)} and 8' = {(0, 10), (5,0)} (c) B={(2,5), (-1, -3)} and 3' = {e1, e2} (d)…

Q: The linear transformation_T:R³ OK² is represented. by the matrix [T]8= 1 20 where B= 012 and B' = 二…

Q: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are there from A to B?…

Q: Prove that translation of an n-dimensional point by multiplication by an n × n matrix is not a…

Q: The matrices A₁ = [J]. - [ ] 4-[61] , 10 form a basis for the linear space V = R²x2. Write the…

Q: IfT: R² R³ is a linear transformation such that -n the standard matrix of Tis 13 T([2])-[3] . and T…

Q: Suppose that T : R² → R² is a matrix transformation and that 7([}))-[-), "([;))-}] 7((:) (a) Find…

Q: uppose is the quadratic form Q = x Ax, where A is the symmetric matrix A = 2 he quadratic form is…

Q: Let T: R² R2 be given by →> Find the matrix M of the inverse linear transformation, T-¹. M = -5 T(x)…

A: Suppose T:R2→R2 is given by T(x)=-1-5-34X (1) To find the matrix M of the inverse linear…

Q: then the standard matrix of T is A = IfT: R² R³ is a linear transformation such that - 22 19 -5 18…

Q: Let T be the function T: R³ R2 given by + (1)-[*] (ED) T (a) Show that T is a linear transformation.…

Q: 3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of…

A: To find the change of coordinates matrix from a basis β′ to β for the vector space VThe identity…

Q: Verify by finding the matrix of S 0 T (a) by direct substitution and (b) by matrix multiplication of…

Q: Find the standard matrix representation for each linear operator L : R^2 → R^2 described below: (a)…

A: Solution is uploaded in next step

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

Q: Let T: R² → R² be defined by T = {[5].[a]} C= Given Pc 1 -2 = [223] -2 5 [T](PB (u)) = Ex: 5 ([2/2])…

Q: Suppose that B = (CEED-·B·CD) -5 and C= 0 are ordered bases of R³. Find the conversion matrix from B…

A: Concept: A vector r is said to be a linear combination of vectors a ,b and c.. etc., if there exist…

Q: Let = A = - = The cross product of two vectors in R³ is defined by a1 a2 az X b₁ b₂ b3 = 0 E] 7 Find…

Q: Find the standard matrix for the linear transformation T (æ, y) = (2x – 3y, x – y, y – 4æ) 3y, æ –…

Q: 2. Find the matrix of the linear operator L: P₂ (R)→ P₂ (R) defined by L(c+bx+ar²) = c+(a+b)x² with…

A: To determine the matrix for a linear transformation. Find the value of linear transformation on…

Q: [1 3 B = 2 1 5 0 A = 0 -5 4 and 3 8 QA + B'.

Question

Let a and B be the standard bases for R" and R" respectively. For
each of the following linear transformations T; : R² → R", compute the
matrix [T;%-
2a
b
()
(a) T1 : R² → R³, T
За + 46
a
() - (*:)
(C)
(C)
(2а + 3b —.
a +b
(b) Т, : R3 — R?, T,
b
(c) T3 : R³ → R', T3
= (2a + b – 3c).
(d) T4 : R" → R", T4

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

part a

VIEW

part b

VIEW

part c

VIEW

Step by step

Solved in 3 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 kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Find a basis for R2 that includes the vector (2,2).
Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
Determine if the following transformations are linear. а)Т (х, у) — (4х — бу,-2х +3у) b)T(x, y, z) = (y-1, x)
Suppose T: R¹→P3 is a linear transformation whose action on a basis for R4 is as follows: -3 a C = II 9x²-12x+6 T 0 0 Describe the action of T on a general vector, using x as the variable for the polynomial and a, b, c, and d as constants. Use the '^' character to indicate an exponent, e.g. ax^2-bx+c. -4x²+4x-4 T −4x³−8x²+14x−14 T 2x³-6x²+5x-2
Let 4-[1] and W-[*] A = w= -[-1³]. Find k so that there exists a vector X whose image under the linear transformation T(x) = Axis w. Note: The image is what comes out of the transformation. k = Find k so that w is a solution of the equation Ax = 0. k =
Calculate 121x dxdy where R is the parallelogram with vertices (0,0), (6,2), (7,6) R 1 -(v — Зи), у 11 -(4v – u) 11 and (1,4) using the transformation x =
Which of the following transformations are linear? yi X] + 10 y2 X2 8x1 Yı 7 y2 3x1 + x2 C. -Xi 0. y2 D. 9x2 %3D y2 E.3 y2 Уз 3 X1 7x1 – 2x2 + 6x3 y2 = 10x2 - 3x3 -4x1 – 9x2 F.- Y3 = |L || || || I| || || || IL || || || A. B.
Consider a linear transformation T from R2 to R² for which (:) -}- T and T Find the matrix A of T. A =
Let T: R² R² be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps v = (1, 3) into (-1,3). Use properties of a linear transformation to calculate T(-3u) = ( T(-3u +9v) = ( " " " ), T(9v) = ( )
Suppose A = -65 -140 30 65 -65 -140 2 a. If possible, complete the following equations; otherwise, enter DNE. -10][3] 30 65 40] f((-10,5)) = f((-10,5)) = and f(x) = Ax. (-10,5) (7,-3) 2 [3] b. The linear transformation facts like multiplication by c. Is the vector (2, -1) an eigenvector for A? choose d. Is the vector (-10, 5) an eigenvector for A? choose e. Are the vectors (2, -1) and (-10, 5) in the same eigenspace? choose f. If the vector (7, k) is an eigenvector for A with eigenvalue -5, then k = in the subspace span{(2, -1)}. If so, what is its associated eigenvalue? If so, what is its associated eigenvalue? g. The linear transformation f acts like multiplication by -5 in the subspace span{ the form . h. Is the vector (-35, 15) an eigenvector for f? choose }. Enter your answer as a coordinate vector of If so, what is its associated eigenvalue?