Let T: R - RS be a linear transformation such that T(1,0,0) = (4, 2, -1),...
6. Let S : R + R3 be the linear transformation which satisfies |(1,0,0) = (1,0,–3), S(0,1,0) = (0,-1,0) and S(0,0,1) = (1,-1, -2). Give an expression for S(x, y, z). 4 Marks] Let S be the basis (1,0,0), (0,1,0), (0,0,1) for R3 and let T be the basis (0,0,1), (0,1,1), (1,1,1) for R. Compute the change of basis matrix s[1]7. (b) Compute the matrices s[S]s and s[ST. 18 Marks)
Let TR-R be a linear transformation such that T(1, 1, 1) = (5.0,-1), TO. -1, 2) = (-5, 2, -1), and 7(1.0, 1) = (1, 0, 1). Find the indicated image 712,-1, 1) T2,-1, 1) = Need Help? Read it Talk to a Tutor Submit Answer
Let T: R3 ? R3 be a linear transformation such that T(1, o, o)-(4,-1,2). TO, 1, o)-(,-2. 3), and To, o. 1)-a,-20·Find the indicated image.
3) Let T be a linear transformation from M22(R) to P3(R). Let B= (4 5] [1 ] [ 2 1]: [4 ;] Let C = (1 + 1x + 0x2 + Or?),(0+10 + 1x2 + 0x3), (0+ 0x + 1x² + 1r), (0+ 0x + 0x² + 1x2) 1 6 - 2 1 8 -8 18 15 Let M= be the matrix transformation of T from basis B to C. 3 -2 -9 6 -2 -12 5 -41 The closed...
4. Let T: R - R be a linear transformation such that 2x1 32 32 3 -1 22 + T3 T 2 Find the standard matrix of T. 5. Compute 3A - 4B, AB and BA: 021 3 1 0 and B -2 0 1 3 2 1 A = 1 -4 1 1 4 0 6. Find the inverse of each matrix BEE 0 1 -2 4 -6 and 1 1 3 -5 3 -1 1
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...
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) []
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...
Find a linear transformation T : R 3 → M22 such that T 1 2 4 = ( 4 1 7 2 ) , T 0 3 5 = ( 0 7 2 4 ) , and T 2 0 2 = ( 1 4 1 3 ) . 9. (4 marks) Find a linear transformation T:R3 M22 such that T | 2 = 1 ( 7 2...
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12