(1 point) Consider a linear transformation 7 from Rto R' for which *([]) = 13) and...
(1 point) Find the matrix A of the linear transformation from R to R given by -(:)-616) A=
7. Consider the linear transformation T : (R) → M2x2 (R) defined by ao 2a2 ao- 3a1 4a0 - 12a1 2ao Find the matrix for T, Ts, where 0 00 00 1 are bases for P2R) and M2x2(R) respectively. Find bases for ker(T) and range(T). Is T one-to-one, onto, neither, or both?
(1 point) Let A- [7 ] Define the linear transformation T: R2 + R by T) = A. Find the following. 1([-])- 7([]) -
2) Let T be a linear transformation from P3(R) to M22(R). Let B= (1+2x + 4x2 + 8x3), (1 + 3x + 5x2 + 10x3), (1 + 4x + 7x2 + 13r%),(1 + 4x + 7x2 + 14x²). Let C= [] [ 1];[1 ] [ ] 0 17 40 Let M= 13 31 36 124 22 52 -61 -209 23 55 -64 -220 be the matrix transformation of T from basis B to C. -47 -161 The closed form of...
(1 point) If T:R → R is a linear transformation such that 13 , T||0||= 01) [ 1] T||1||= -1, Uo4 -4 i 2 1 T||0||= (11) then T|| -2
(1 point) Find the matrix A of the linear transformation from R2 to Rºgiven by -6 -5 21 T 1 21+ 7 22 22 3 5 A=
Consider the linear transformation from R² to Rº given by L(21,3) = (31 +232, 21 – 22). I (a) In the standard basis for R2 and R, what is the matrix A that corresponds to the linear transformation L? (5 points) (b) Let U = {(1,1), (-1,2)}. Find the transition matrix from U to the star dard basis for R. (5 points) (c) Let V = {(1,0), (-1,1)). Find the transition matrix from the standard basis for R2 to V....
For each transformation below, find the value of T(U). 1) Let T be a linear transformation from R$ to M2 (R) 2 Let B= -1 2 3 Let C= [1].[133] [131] 1 -22 -21 -22 -21 -59 14 13 Let M= be the matrix transformation of T from basis B to C 37 -59 30 30 -19 -1 Let v= 2 2 The value of T(0) = 2) Let T be a linear transformation from P3 (R) to M22(R). Let...
7. (4 points) Let T R -R' be linear transformation such that Find YORK UNIVERSITY PACULTY OF SCIENCE 8. (4 points) Determine whether the following transformation TR' answer. If it is linear, express it is a matrix transformation R' is linear. Justify your (a) 61-[2] "[:] [3] -[:]-[8) []
QUESTION 1. §1.9 THE MATRIX OF A LINEAR TRANSFORMATION Le t T R be the linear transformation defined by t-th AnSwer Find the standard matrix of T. Is T one to one? Is T onto? Jushif'cahon